U.S. patent application number 12/886745 was filed with the patent office on 2011-01-13 for actuatable capacitive transducer for quantitative nanoindentation combined with transmission electron microscopy.
This patent application is currently assigned to HYSITRON INCORPORATED. Invention is credited to S.A. Syed Asif, Edward Cyrankowski, Kalin Kounev, Oden L. Warren.
Application Number | 20110005306 12/886745 |
Document ID | / |
Family ID | 38332641 |
Filed Date | 2011-01-13 |
United States Patent
Application |
20110005306 |
Kind Code |
A1 |
Warren; Oden L. ; et
al. |
January 13, 2011 |
ACTUATABLE CAPACITIVE TRANSDUCER FOR QUANTITATIVE NANOINDENTATION
COMBINED WITH TRANSMISSION ELECTRON MICROSCOPY
Abstract
An actuatable capacitive transducer including a transducer body,
a first capacitor including a displaceable electrode and
electrically configured as an electrostatic actuator, and a second
capacitor including a displaceable electrode and electrically
configured as a capacitive displacement sensor, wherein the second
capacitor comprises a multi-plate capacitor. The actuatable
capacitive transducer further includes a coupling shaft configured
to mechanically couple the displaceable electrode of the first
capacitor to the displaceable electrode of the second capacitor to
form a displaceable electrode unit which is displaceable relative
to the transducer body, and an electrically-conductive indenter
mechanically coupled to the coupling shaft so as to be displaceable
in unison with the displaceable electrode unit.
Inventors: |
Warren; Oden L.; (New
Brighton, MN) ; Asif; S.A. Syed; (Bloomington,
MN) ; Cyrankowski; Edward; (Woodbury, MN) ;
Kounev; Kalin; (Shoreview, MN) |
Correspondence
Address: |
DICKE, BILLIG & CZAJA
FIFTH STREET TOWERS, 100 SOUTH FIFTH STREET, SUITE 2250
MINNEAPOLIS
MN
55402
US
|
Assignee: |
HYSITRON INCORPORATED
Minneapolis
MN
|
Family ID: |
38332641 |
Appl. No.: |
12/886745 |
Filed: |
September 21, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11672489 |
Feb 7, 2007 |
7798011 |
|
|
12886745 |
|
|
|
|
60771560 |
Feb 8, 2006 |
|
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Current U.S.
Class: |
73/81 |
Current CPC
Class: |
G01B 7/22 20130101; G01N
2203/0617 20130101; G01Q 60/366 20130101; H01J 2237/20264 20130101;
G01Q 30/02 20130101; G01N 3/42 20130101; G01N 2203/0051 20130101;
G01N 2203/0286 20130101; G01D 5/2417 20130101; H02N 1/002
20130101 |
Class at
Publication: |
73/81 |
International
Class: |
G01N 3/48 20060101
G01N003/48 |
Goverment Interests
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0002] This invention may be related to work done with Government
support under Grant No. DE-FG02-04ER83979 awarded by the Department
of Energy.
Claims
1. A method of quantitative nanoindentation combined with
transmission electron microscopy comprising: indenting a sample by
actuating an actuatable capacitive transducer, wherein actuating
includes adjusting voltages supplied to the actuatable capacitive
transducer; recording signals required to generate a representation
of a force-displacement relationship; and recording a stream of
transmission electron microscopy images illustrating one or more
aspects of indenting the sample.
2. The method of claim 1, wherein the representation of a
force-displacement relationship comprises a force-displacement
curve.
3. The method of claim 2, wherein the force-displacement curve
comprises a contact force versus a penetration depth curve.
4. The method of claim 1, further comprising recording a time while
indenting the sample to generate a representation of a force-time
relationship.
5. The method of claim 4, wherein the representation of a
force-time relationship comprises a contact force versus time
curve.
6. The method of claim 1, further comprising recording a time while
indenting the sample to generate a representation of a
displacement-time relationship.
7. The method of claim 6, wherein the representation of a
displacement-time relationship comprises a penetration depth versus
time curve.
8. A method of quantitative nanoindentation combined with
transmission electron microscopy comprising: indenting a sample by
actuating an actuatable capacitive transducer; controlling a
displacement resulting from actuating the actuatable capacitive
transducer; recording signals required to generate a
force-displacement curve; and recording a stream of transmission
electron microscopy images illustrating one or more aspects of
indenting the sample.
9. The method of claim 8, wherein the force-displacement curve
comprises a contact force versus a penetration depth curve.
10. The method of claim 8, wherein controlling the displacement
involves feedback means and optionally feedforward means.
11. The method of claim 8, further comprising recording a time
while indenting the sample to generate a force-time curve and/or a
displacement-time curve.
12. A method of quantitative nanoindentation combined with
transmission electron microscopy comprising: indenting a sample by
actuating an actuatable capacitive transducer; controlling a
contact force resulting from indenting the sample; recording
signals required to generate a curve representative of the contact
force versus a penetration depth; and recording a stream of
transmission electron microscopy images illustrating one or more
aspects of indenting the sample.
13. The method of claim 12, wherein controlling the contact force
involves feedback means and optionally feedforward means.
14. The method of claim 12, further comprising recording a time
while indenting the sample to generate a curve representative of
the contact force versus the time and/or a curve representative of
the penetration depth versus the time.
15. A method of quantitative nanoindentation combined with
transmission electron microscopy comprising: indenting a sample by
actuating a piezoelectric actuator while operating an actuatable
capacitive transducer in a single-sided force-feedback control
mode; recording signals required to generate a contact force versus
penetration depth curve; and recording a stream of transmission
electron microscopy images illustrating one or more aspects of
indenting the sample.
16. The method of claim 15, further comprising recording a time
while indenting the sample to generate a contact force-time curve
and/or a penetration depth-time curve.
17. The method of claim 15, wherein operating the actuatable
capacitive transducer in the single-sided force-feedback control
mode generally prevents a displaceable electrode of the actuatable
capacitive transducer from displacing relative to a transducer body
of the actuatable capacitive transducer.
18. A method of quantitative nanoindentation combined with
transmission electron microscopy comprising: indenting a sample by
actuating a piezoelectric actuator while operating an actuatable
capacitive transducer in a double-sided force-feedback control
mode; recording signals required to generate a force-displacement
curve; and recording a stream of transmission electron microscopy
images illustrating one or more aspects of indenting the
sample.
19. The method of claim 18, further comprising recording a time
while indenting the sample to generate a force-time curve and/or a
displacement-time curve.
20. The method of claim 18, wherein operating the actuatable
capacitive transducer in the double-sided force-feedback control
mode generally prevents a displaceable electrode of the actuatable
capacitive transducer from displacing relative to a transducer body
of the actuatable capacitive transducer and wherein recording
signals includes recording a feedback voltage ideally proportional
to a contact force.
21. A method of quantitative nanoindentation combined with
transmission electron microscopy comprising: indenting a sample by
actuating an actuatable capacitive transducer; controlling a
contact force resulting from indenting the sample whenever the
contact force is above a specified contact force and controlling a
displacement resulting from actuating the actuatable capacitive
transducer whenever the contact force is below the specified
contact force; recording signals required to generate a contact
force versus penetration depth curve; and recording a stream of
transmission electron microscopy images illustrating one or more
aspects of indenting the sample.
22. The method of claim 21, further comprising recording a time
while indenting the sample to generate a contact force versus time
curve and/or a penetration depth versus time curve.
23. The method of claim 21, wherein controlling the contact force
and/or controlling the displacement involves feedback means and
optionally feedforward means.
24. A method of quantitative nanoindentation combined with
transmission electron microscopy comprising: indenting a sample;
recording signals required to generate a contact force versus a
penetration depth curve; and recording a stream of electron
diffraction patterns illustrating one or more aspects of indenting
the sample.
25. The method of claim 24, further comprising recording a time
while indenting the sample to generate a contact force versus time
curve and/or a penetration depth versus time curve.
26. A method of positioning an indenter relative to a substantially
wedge-shaped sample having a plateau, a first inclined sidewall,
and a second inclined sidewall, the method comprising: using the
indenter to generate a scanning probe microscopy topography image
illustrating a portion of the plateau, a portion of the first
inclined sidewall, and a portion of the second inclined sidewall;
determining a three-dimensional spatial orientation of the plateau
from the image; determining a width of the plateau from the image;
and positioning the indenter relative to the plateau using the
width of the plateau and the three-dimensional spatial orientation
of the plateau as a guide.
27. The method of claim 26, wherein positioning the indenter
relative to the plateau places the indenter in close proximity to
or in contact with the plateau at a location illustrated in the
image.
28. The method of claim 26, wherein positioning the indenter
relative to the plateau places the indenter in close proximity to
or in contact with the plateau at a location not illustrated in the
image.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This Utility patent application is a Divisional application
of U.S. patent application Ser. No. 11/672,489, filed Feb. 7, 2007,
which claims benefit from U.S. Provisional Patent Application No.
60/771,560, filed Feb. 8, 2006, priority to which is claimed under
35 U.S.C. .sctn.119(e) and which are both incorporated herein by
reference.
BACKGROUND
[0003] Each reference from the following list of references is
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Nanoindentation (Springer, New York, 2004). ("Reference 1") [0005]
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Chraska, R. Hull, J. W. Morris, Jr., A. Zettl, and U. Dahmen,
Microsc. Microanal. 7, 507 (2001). ("Reference 8") [0012] 9.
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1625 (2001). ("Reference 9") [0013] 10. "In-situ transmission
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materials", A. Minor, E. Lilleodden, M. Jin, E. Stach, D. Chrzan,
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3626 (2004). ("Reference 14") [0018] 15. "Effects of solute Mg on
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[0021] 18. "Indentation mechanics of Cu--Be quantified by an in
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Oleg Lourie, Gatan Inc. ("Reference 20") [0024] 21. ISO
14577-1:2002 ("Metallic materials--instrumented indentation test
for hardness and materials parameters--part 1: test method"); ISO
14577-2:2002 ("Metallic materials--instrumented indentation test
for hardness and materials parameters--part 2: verification and
calibration of testing machines"); ISO 14577-3:2002 ("Metallic
materials--instrumented indentation test for hardness and materials
parameters--part 3: calibration of reference blocks"). ("Reference
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"TriboIndenter.RTM.: nanomechanical test instruments"; brochure
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"TriboScope.RTM.: quantitative nanomechanical testing for AFMs".
("Reference 26") [0030] 27. "A new force sensor incorporating
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Joyce and J. E. Houston, Rev. Sci. Instrum. 62, 710 (1991).
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J. F. Graham, and P. R. Norton, Phys. Can. 54, 122 (1998).
("Reference 28") [0032] 29. "Apparatus for microindentation
hardness testing and surface imaging incorporating a multi-plate
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measurements using a capacitive transducer system in atomic force
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Wyrobek, Philos. Mag. A 74, 1117 (1996). ("Reference 32") [0036]
33. For example: "Vertical comb-finger capacitive actuation and
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35. "A rocking beam electrostatic balance for the measurement of
small forces", G. L. Miller, J. E. Griffith, E. R. Wagner, and D.
A. Grigg, Rev. Sci. Instrum. 62, 705 (1991). ("Reference 35")
[0039] 36. "High-resolution capacitive load-displacement transducer
and its application in nanoindentation and adhesion measurements",
N. Yu, W. A. Bonin, and A. A. Polycarpou, Rev. Sci. Instrum. 76,
045109 (2005). ("Reference 36") [0040] 37. "Tapping mode imaging
with an interfacial force microscope", O. L. Warren, J. F. Graham,
and P. R. Norton, Rev. Sci. Instrum. 68, 4124 (1997). ("Reference
37") [0041] 38. "Nanoindentation and contact stiffness measurement
using force modulation with a capacitive load-displacement
transducer", S. A. S. Asif, K. J. Wahl, and R. J. Colton, Rev. Sci.
Instrum. 70, 2408 (1999). ("Reference 38") [0042] 39. "Quantitative
imaging of nanoscale mechanical properties using hybrid
nanoindentation and force modulation", S. A. S. Asif, K. J. Wahl,
R. J. Colton, and O. L. Warren, J. Appl. Phys. 90, 1192 (2001);
Erratum 90, 5838 (2001). ("Reference 39") [0043] 40.
"High-performance drive circuitry for capacitive transducers", W.
Bonin, U.S. Pat. No. 6,960,945. ("Reference 40")
[0044] Nanoindentation (see References 1 and 2), today's primary
technique for probing small volumes of solids for the purpose of
quantifying their mechanical properties, involves the use of an
instrument referred to as a nanoindenter to conduct a
nanoindentation test. At a minimum, a nanoindentation test entails
a gradual loading followed by a gradual unloading of a sharp
indenter against a sample. The indenter is usually made of diamond,
diamond being both the stiffest and the hardest known material. The
indenter is shaped to a well-defined geometry typically having an
apical radius of curvature in the range of 50-100 nm. The most
prevalent indenter geometry is the three-sided pyramidal Berkovich
geometry, which imposes a representative strain of .about.7% if
perfectly formed.
[0045] A hallmark of nanoindentation is the acquisition throughout
the nanoindentation test of both the force applied to the sample
(peak load typically <10 mN) and the indenter displacement into
the sample (maximum penetration depth typically <10 .mu.m) to
generate a force-displacement curve. High-performance nanoindenters
exhibit force and displacement noise floors below 1 .mu.N RMS and 1
nm RMS, respectively. The sample's mechanical properties, such as
elastic modulus and hardness, can be evaluated by analyzing the
force-displacement curve, the most common method of analysis being
the elastic unloading analysis published by Oliver and Pharr (see
Reference 3) in 1992.
[0046] Nanoindentation suffers from a major shortcoming, however.
Despite more than a decade's worth of maturation, nanoindentation
still leaves much to be desired in terms of providing definitive
mechanistic explanations for certain features of its outputted
force-displacement curves. For example, the commonly observed
load-controlled nanoindentation phenomenon of a pop-in transient
(see Reference 4), a sudden sizeable increase in penetration depth
without a corresponding increase in load, an event signaling
discontinuous yielding, has many possible interpretations:
dislocation burst, shear band formation, fracture onset, spalling,
stress-induced phase transformation, etc. Because it is extremely
difficult to image such discrete nano-to-atomistic scale happenings
at their moments of occurrence, it is not surprising that the
scientific literature is replete with examples of deformation
mechanisms assigned to pop-in transients with little more to go on
than knowledge of the nature of the sample under investigation in
combination with educated speculation. The invention provides the
opportunity to make unambiguous the microscopic origin of a pop-in
transient, or that of any other encountered nanoindentation
phenomenon, by coupling nanoindentation to a TEM in an in-situ
manner (see Reference 5). Doing so required meeting a set of
configurational and environmental challenges not anticipated by
existing nanoindentation transducers.
[0047] Configurational challenges presented by TEMs include: (1)
severely restricted space mandating a nanoindentation transducer
considerably more miniature than those currently supplied with
commercial nanoindenters; (2) achieving acceptably high maximums in
load and penetration depth in spite of the limited size of the
transducer; (3) the need to operate the transducer with its
indenter horizontal rather than in the standard vertical
orientation; (4) the requirement that the indenter extend
significantly from the transducer's body to reach well into the
TEM's pole piece gap, which necessitates means for countering the
associated tilting moment; (5) the requirement that the transducer
be largely insensitive with respect to being rotated about the
indenter's axis; and (6) the requirement that the transducer
achieve high performance in spite of long wiring runs from the
transducer residing in vacuum to its electronic circuitry residing
out of vacuum, the longer the wiring runs, the greater the
likelihood of electromagnetic interference pick-up and capacitive
signal loading.
[0048] Environmental challenges presented by TEMs include: (1) high
vacuum (e.g., 10.sup.-7 torr) limiting construction materials to
those not prone to outgassing; (2) the requirement that the
transducer not seriously impede the pumping conductance of the TEM
holder so that high vacuum can be achieved in a sensible period of
time; (3) high vacuum restricting actuation/sensing strategies to
those generating minimal heat; (4) high vacuum increasing the
transducer's mechanical quality factor (Q) to a value much higher
than in air, the higher the quality factor, the longer the
impulse-ring-down time; (5) the presence of a highly energetic
electron beam (e.g., 300 kV) impinging the indenter, which
necessitates means for bleeding charge from the indenter; and (6)
the presence of an especially strong magnetic field (e.g., 2 tesla
in magnitude) restricting actuation/sensing strategies to those not
relying on magnetic principles, and limiting construction materials
to those without ferromagnetic content.
[0049] Owing to the severe set of challenges to overcome, previous
attempts at in-situ TEM nanoindentation (see References 6-20) have
been limited to qualitative or semi-quantitative experimentation.
Qualitative in-situ TEM nanoindentation refers to viewing/recording
a stream of TEM images that show how a sample deforms during the
nanoindentation process without having the technology to acquire a
corresponding force-displacement curve. The inability to acquire a
force-displacement curve renders this experimental approach of low
relevance to the invention. Semi-quantitative in-situ TEM
nanoindentation also refers to viewing/recording a stream of TEM
images that show how a sample deforms during the nanoindentation
process, but with the added dimension of acquiring a corresponding
force-displacement curve of poor accuracy relative to metrological
standards established for nanoindentation, such as those expressed
in ISO 14577 (see Reference 21).
[0050] Further discussion of semi-quantitative nanoindentation
helps to clarify the meaning of quantitative nanoindentation
(quantitative nanoindentation is often referred to as depth-sensing
indentation). The in-situ TEM nanoindenter manufactured by
Nanofactory Instruments AB (TEM-Nanoindentor: SA2000.N (see
References 19 and 20)) is a highly relevant example of a
semi-quantitative nanoindenter. Nanofactory's instrument is at odds
with metrological standards established for nanoindentation on
account of the series loading configuration it adopts. The series
loading configuration poses a problem because it does not provide a
direct measure of penetration depth. Instead, ignoring factors such
as load frame compliance and thermally-induced relative position
drift, the penetration depth is equal to the motion provided by an
actuator minus the deflection associated with a device inferring
load. The change in deflection is virtually equal to the change in
motion in the limit of high contact stiffness, where "high" means
high relative to the spring constant of the deflectable device
inferring load. Consequently, it is virtually impossible to resolve
changes in penetration depth in the high contact stiffness limit, a
limit very easily reached. In contrast, quantitative nanoindenters
exhibit constant penetration depth resolution regardless of the
value of the contact stiffness.
[0051] To further complicate matters, Nanofactory's instrument
relies on a piezoelectric actuator to affect the indenter-sample
separation, but the instrument does not have a displacement sensor
dedicated to measuring the actuator's extension or contraction (see
Reference 20). Computing a piezoelectric actuator's extension or
contraction from the voltage applied to the actuator has been shown
to be unreliable because such actuators exhibit non-linearity,
hysteresis, and creep dependent on the history of use (see
Reference 22). Sequential analysis of TEM images that show the
indenter penetrating the sample seems to be a viable way of
directly quantifying the penetration depth in the absence of direct
depth sensing. However, our own experience tells us this method is
inconvenient and of dubious accuracy. Moreover, the indenter cannot
be seen in dark-field TEM images. Operationally, Nanofactory's
instrument is reminiscent of an atomic force microscope (AFM)
conducting nanoindentation. There is a long history of AFMs
delivering faulty force-displacement curves partially on account of
the difficulties just mentioned (see References 23 and 24).
[0052] In Nanofactory's instrument, the deflectable device
inferring load is a miniature two-plate capacitive transducer (see
Reference 25) comprising a stationary electrode and a
spring-supported displaceable electrode to which the indenter is
attached perpendicularly; "stationary" and "displaceable" mean
stationary and displaceable with respect to the transducer's body.
The displaceable electrode's deflection is determined by monitoring
the change in capacitance. Multiplying the displaceable electrode's
deflection by the spring constant of the springs supporting the
displaceable electrode yields the force acting on the indenter.
Curiously, Nanofactory's instrument does not capitalize its
potential for electrostatic actuation (see Reference 20), which
prevents it from employing a loading configuration other than the
inappropriate series loading configuration.
[0053] A suite of nanoindenters manufactured by Hysitron, Inc. (see
Reference 26) and the interfacial force microscope (IFM) (see
References 27 and 28) originating from Sandia National Laboratories
are scanning nanoindenters utilizing actuatable capacitive
transducers. Both types of instruments are capable of raster
scanning the indenter to image a sample's surface in the manner of
an AFM. Useful information regarding deformation mechanisms can be
obtained from post-test images of the indent's topography, but such
images illustrate no more than the residual deformation field. At
the heart of Hysitron's nanoindenters is a patented three-plate
capacitive transducer (see References 29-32) comprising two
stationary electrodes and a spring-supported displaceable electrode
to which the indenter is attached perpendicularly; "stationary" and
"displaceable" mean the same as before. The electrodes are
components of a three-plate stack, the displaceable electrode being
an element of the center plate. Each stationary electrode has a
center hole, one center hole passing through the indenter without
hindrance and the other center hole with the purpose of equalizing
electrode areas. The dual capability of electrostatic actuation and
capacitive displacement sensing is a hallmark of Hysitron's
three-plate capacitive transducer. Electrostatic actuation in this
case refers to generating an electrostatic force between the
displaceable electrode and the stationary electrode through which
the indenter passes, which deflects the displaceable electrode with
respect to the stationary electrodes. Capacitive displacement
sensing in this case refers to sensing the deflection using the
well-established differential capacitance half-bridge method
involving all three electrodes now widely adopted by
microelectromechanical systems (MEMS) (see Reference 33).
[0054] Hysitron's nanoindenters adopt a parallel loading
configuration, meaning contact stiffness in parallel with the
spring constant of the support springs. This loading configuration
results in the transducer's capacitive displacement sensing output
providing a direct measure of penetration depth, again ignoring
factors such as load frame compliance and thermally-induced
relative position drift. The calculation of contact force involves
the applied electrostatic force and the spring force, the spring
force being related to the product of the easily-calibrated spring
constant of the support springs and the displaceable electrode's
deflection.
[0055] At the heart of the IFM is a differential-capacitance
displacement sensor (see Reference 27) (IFM sensor for brevity)
comprised of two co-planar stationary electrodes facing a
torsion-bar-supported rotatable electrode; "stationary" and
"rotatable" mean stationary and rotatable with respect to the
sensor's body. The rotatable electrode together with a pair of
torsion bars extending from opposing edges of the rotatable
electrode resembles a torsional pendulum. The indenter is attached
perpendicularly to the outer face of the rotatable electrode at a
position equivalent to one stationary electrode's center. A
hallmark of the IFM is its operation as a torque balance. An
electrostatic-force-feedback controller is used to servo the
indenter-side electrostatic torque to continuously suppress the
rotatable electrode from rotating under the influence of the
indenter-sample torque; the non-indenter-side electrostatic torque
is held constant by the controller. The well-established
differential capacitance half-bridge method involving all three
electrodes is used to sense the rotational displacement of the
rotatable electrode. But the action of the controller continuously
nulls the sensor's capacitive displacement sensing output. The
rocking beam sensor (see References 34 and 35) originating from
Bell Laboratories is similar to the IFM sensor, but is used for
critical dimensional metrology rather than for nanoindentation.
[0056] IFMs use a piezoelectric actuator to affect the
indenter-sample separation. The motion provided by the
piezoelectric actuator in combination with the stiffening action of
the electrostatic-force-feedback controller permits direct control
of penetration depth, once more ignoring factors such as load frame
stiffness and thermally-induced relative position drift. IFMs
currently do not have a displacement sensor dedicated to measuring
the piezoelectric actuator's extension or contraction;
nevertheless, IFMs are quantitative nanoindenters from the
viewpoint of loading configuration. Solving the relevant torque
balance equation yields the contact force. The rotational spring
constant of the torsion bars does not enter into the calculation of
contact force because the rotatable electrode is suppressed from
rotating.
[0057] The IFM sensor is currently too large to be housed in a TEM
holder; furthermore, the baseline control effort needed to maintain
an extended-length indenter in the horizontal orientation will be
highly dependent on TEM-holder rotation angle, as will be the
maximum load available for nanoindentation. Nevertheless,
actuatable capacitive transducers are highly attractive for
quantitative in-situ TEM nanoindentation because their operation is
not based on magnetic principles, they draw very little electrical
current, thus they generate very little heat, and they possess
favorable scaling laws for miniaturization.
[0058] The Detailed Description of the invention discloses a novel
actuatable capacitive transducer in addition to other novel aspects
of the invention. Yu et al. made an initial public disclosure on an
alternative actuatable capacitive transducer in the on-line version
of Reference 36 on Mar. 28, 2005. The Yu et al. alternative
actuatable capacitive transducer clearly is not suitable for
quantitative in-situ TEM nanoindentation as disclosed.
[0059] For these and other reasons there is a need for the present
invention.
SUMMARY
[0060] One aspect of the present invention relates to an actuatable
capacitive transducer which enables quantitative in-situ
nanoindentation in a transmission electron microscope (TEM). The
quantitative in-situ TEM nanoindentation technique involves
indenting a sample to acquire a quantitative force-displacement
curve and simultaneously viewing/recording a stream of TEM images
that show how the sample deforms while being indented. This
simultaneous capability permits, for example, a direct correlation
of a specific transient feature of the force-displacement curve to
the sample's sudden change in microstructure.
[0061] In one embodiment, the present invention provides an
actuatable capacitive transducer including a transducer body, a
first capacitor including a displaceable electrode and electrically
configured as an electrostatic actuator, and a second capacitor
including a displaceable electrode and electrically configured as a
capacitive displacement sensor, wherein the second capacitor
comprises a multi-plate capacitor. The actuatable capacitive
transducer further includes a coupling shaft configured to
mechanically couple the displaceable electrode of the first
capacitor to the displaceable electrode of the second capacitor to
form a displaceable electrode unit which is displaceable relative
to the transducer body, and an electrically-conductive indenter
mechanically coupled to the coupling shaft so as to be displaceable
in unison with the displaceable electrode unit.
BRIEF DESCRIPTION OF THE DRAWINGS
[0062] FIG. 1 is a cross-sectional drawing of one embodiment of an
actuatable capacitive transducer of the invention.
[0063] FIG. 2 is an exploded-view drawing of a multi-plate
capacitor of the actuatable capacitive transducer depicted in FIG.
1.
[0064] FIG. 3 is an exploded-view drawing of the center plate of a
multi-plate capacitor of the actuatable capacitive transducer
depicted in FIG. 1.
[0065] FIG. 4 is a multi-plate capacitor of the actuatable
capacitive transducer depicted in FIG. 1: a) fully-assembled
drawing; and b) photograph of a built multi-plate capacitor showing
its size relative to a US dime.
[0066] FIG. 5 is additional perspectives of the actuatable
capacitive transducer depicted in FIG. 1: a) exploded-view drawing;
and b) fully-assembled drawing.
[0067] FIG. 6 illustrates the major aspects of the electrical
configuration of the actuatable capacitive transducer depicted in
FIG. 1. Relative dimensions of the actuatable capacitive transducer
are improper for the sake of clarity.
[0068] FIG. 7 is a photograph of a built nanoindentation head.
[0069] FIG. 8 is a built TEM holder: a) photograph of the holder
shown in entirety;
[0070] b) photograph showing the tongue portion of the holder in
detail; and c) photograph showing the holder inserted into a JEOL
JEM 3010 TEM.
[0071] FIG. 9 is a block diagram for a nanoindentation head's
control system.
[0072] FIG. 10 is a built actuatable capacitive transducer's
transient response in a JEOL JEM 3010 TEM: a) out-of-contact
impulse-ring-down trace for the open-loop mode; including the
exponential decay of the trace's envelope; and b) out-of-contact
step-response trace while using the displacement control mode.
[0073] FIG. 11 illustrates means for bleeding charge from a
conductive indenter when operating in a JEOL JEM 3010 TEM and
compares quantitative in-situ TEM cantilever bending data for two
electrical configurations: a) drawing of a proper electrical
configuration; b) force-displacement curve while using the
displacement control mode, for an improper electrical
configuration; and c) force-displacement curve while using the
displacement control mode, for the proper electrical configuration
depicted in a).
[0074] FIG. 12 is a set of quantitative in-situ TEM nanoindentation
data for nanograin aluminum obtained with a built actuatable
capacitive transducer operating in a JEOL JEM 3010 TEM: a)
force-displacement curve while using the displacement control mode;
b) force-displacement curve while using the single-sided
force-feedback control mode; and c) two video frames extracted from
a recorded stream of TEM images that correlates to the
force-displacement curve in a).
[0075] FIG. 13 is a set of quantitative in-situ TEM nanoindentation
data for single-crystal silicon obtained with a built actuatable
capacitive transducer operating in a JEOL JEM 3010 TEM: a)
force-displacement curve while using the displacement control mode;
and b) post-test TEM image and electron diffraction patterns.
DETAILED DESCRIPTION
[0076] In the following Detailed Description, reference is made to
the accompanying drawings which form a part hereof, and in which is
shown by way of illustration specific embodiments in which the
invention may be practiced. In this regard, directional
terminology, such as "top," "bottom," "front," "back," "leading,"
"trailing," etc., is used with reference to the orientation of the
Figure(s) being described. Because components of embodiments of the
present invention can be positioned in a number of different
orientations, the directional terminology is used for purposes of
illustration and is in no way limiting. It is to be understood that
other embodiments may be utilized and structural or logical changes
may be made without departing from the scope of the present
invention. The following detailed description, therefore, is not to
be taken in a limiting sense, and the scope of the present
invention is defined by the appended claims.
[0077] An actuatable capacitive transducer suitable for
quantitative in-situ TEM nanoindentation is one novel aspect of the
invention. A detailed description of one or more embodiments of an
actuatable capacitive transducer according to the present invention
follows.
[0078] FIG. 1 is a cross-sectional drawing of one embodiment of an
actuatable capacitive transducer 30 according to the present
invention. Actuatable capacitive transducer 30 includes an
electrically conductive transducer body 32, a first multi-plate
capacitor 34, a second multi-plate capacitor 36, and a coupling
shaft 46. First and second multi-plate capacitors 34 and 36 are
attached to conductive transducer body 32, without electrically
shorting them to conductive transducer body 32, such that they are
maintained at a fixed separation and are substantially parallel to
each other. In one embodiment, conductive transducer body 32 is
made of titanium.
[0079] As will be described in greater detail below with respect to
FIG. 1 and FIG. 2, first and second multi-plate capacitors 34 and
36 respectively include center plates 38 and 40, and each include a
displaceable electrode 42 supported from a frame 43 by springs 44,
where "displaceable" means displaceable relative to conductive
transducer body 32. Coupling shaft 46, as will be described in
greater detail below with respect to FIG. 1 and FIG. 2,
mechanically couples the displaceable electrodes 42 to form a
mechanically-coupled displaceable electrode unit, wherein the
mechanically-coupled displaceable electrode unit is displaceable as
one unit relative to conductive transducer body 32. In one
embodiment, coupling shaft 46 comprises an electrically conductive
threaded rod 48 encased, except at its two ends, by a tightly
adhered dielectric (electrically insulating) sheath 50. Dielectric
sheath 50 is mechanically stiff in order to suppress conductive
threaded rod 48, which has a high ratio of length to diameter, from
flexing under the influence of a force. Dielectric sheath 50 also
electrically insulates conductive threaded rod 48 from the
displaceable electrodes 42. In one embodiment, conductive threaded
rod 48 is made of brass and dielectric sheath 50 is made of
Macor.RTM., a machinable ceramic.
[0080] In one embodiment, as illustrated by FIG. 1, actuatable
capacitive transducer 30 further includes a dielectric sleeve 52, a
dielectric standoff 54, a probe wire tab 56, and an electrically
conductive nut 58. Dielectric sleeve 52 reinforces the connection
of coupling shaft 46 to the displaceable electrode 42 of first
multi-plate capacitor 34. Dielectric standoff 54 reinforces the
connection of coupling shaft 46 to the displaceable electrode 42 of
second multi-plate capacitor 36 and serves as a base for probe wire
tab 56. Probe wire tab 56 slips over an unsheathed end of
conductive threaded rod 48 which is located internally to
conductive transducer body 32 and is retained against dielectric
standoff 54 by screwing on conductive nut 58, such that probe wire
tab 56 is in intimate electrical contact with conductive threaded
rod 48. In one embodiment, dielectric sleeve 52 and dielectric
standoff 54 are each made of Macor.RTM., probe wire tab 56 is made
of beryllium copper, and conductive nut 58 is made of brass.
[0081] In one embodiment, as illustrated by FIG. 1, actuatable
capacitive transducer 30 includes an electrically conductive probe
60. In one embodiment, conductive probe 60 includes an electrically
conductive indenter 62 which is mechanically and electrically
coupled to an electrically conductive shank 64. Conductive shank 64
is tapped to mate with conductive threaded rod 48 and includes a
vent hole 66 to prevent a virtual leak in the high-vacuum
environment of a TEM. A portion of conductive shank 64 is square in
cross-section (see FIG. 5a) for insertion into a probe mounting
tool designed similarly to a nut driver. In one embodiment,
conductive probe 60 is screwed onto an unsheathed end of conductive
threaded rod 48 which is located externally to conductive
transducer body 32, such that conductive probe 60 is in intimate
electrical contact with conductive threaded rod 48. It is noted
that the ability to screw conductive probe 60 on and off conductive
threaded rod 48 facilitates probe storage or probe exchange
whenever necessary. In one embodiment, conductive shank 64 is made
of titanium and conductive indenter 62 is made of diamond highly
through doped with boron and ground to a well-defined geometry,
such as the Berkovich geometry, for example. A standard method of
attaching a diamond indenter to a titanium shank involves vacuum
brazing.
[0082] FIG. 2 is an exploded-view drawing of one embodiment of a
multi-plate capacitor according to the present invention, such as
first multi-plate capacitor 34 of FIG. 1. It is noted that the
illustration of FIG. 2 and the following description also applies
to second multi-plate capacitor 36. In addition to center plate 38,
first multi-plate capacitor 34 includes a first outer plate 70, a
second outer plate 72, which is substantially identical to first
outer plate 70, a first dielectric spacer 74, and a second
dielectric spacer 76, which is substantially identical to first
dielectric spacer 74. In one embodiment, first and second outer
plates 70 and 72 each comprise a dielectric slab having a
stationary electrode 80 in the shape of a ring patterned onto one
face of the dielectric slab, a guard ring 82 patterned around
stationary electrode 80, and a ground plane 84 patterned onto the
opposite face of the dielectric slab. The term "stationary", with
regard to stationary electrode 80, means stationary relative to the
conductive transducer body 32. In one embodiment, first and second
outer plates 70 and 72 are made of TMM.RTM. 4 patterned with
electro-deposited copper cladding, TMM.RTM. 4 being a
ceramic/polytrifluoroethylene laminate often used in outer space
applications, and first and second dielectric spacers 74 and 76 are
made of aluminum heavily anodized to achieve electrically
insulating surfaces.
[0083] First and second outer plates 70 and 72, and center plate 38
each include a center hole 86. In one embodiment, center hole 86 of
center plate 38 is smaller in diameter than center holes 86 of
first and second outer plates 70 and 72, as indicated by the pair
of vertical dashed lines in FIG. 2.
[0084] Multi-plate capacitor 34 is constructed as a stack in the
order of first outer plate 70, first dielectric spacer 74, center
plate 38, second dielectric spacer 76, and second outer plate 72.
Again, it is noted that the following description applies to both
first and second multi-plate capacitors 34 and 36. Stationary
electrode 80 of first outer plate 70 faces one face of displaceable
electrode 42 of center plate 38. Stationary electrode 80 (not shown
in FIG. 2) of second outer plate 72 faces the opposite face of
displaceable electrode 42 of center plate 38. First dielectric
spacer 74 separates and electrically insulates first outer plate 70
from center plate 38. Second dielectric spacer 76 separates and
electrically insulates second outer plate 72 from center plate 38.
The thickness of first dielectric spacer 74 is a dominant factor in
determining a first electrode gap, corresponding to the separation
between stationary electrode 80 of first outer plate 70 and
displaceable electrode 42, and the thickness of second dielectric
spacer 76 is a dominant factor in determining a second electrode
gap, corresponding to the separation between stationary electrode
80 of second outer plate 72 and displaceable electrode 42.
[0085] From a mechanical design viewpoint, first and second
multi-plate capacitors 34 and 36 may differ with respect to the
thickness of dielectric spacers 74 and 76. In one embodiment,
dielectric spacers 74 and 76 of the first multi-plate capacitor 34
each have a thickness of 100 .mu.m, and dielectric spacers 74 and
76 of second multi-plate capacitor 36 each have a thickness of 75
.mu.m. In this embodiment, the difference in thickness between
dielectric spacers 74 and 76 of first and second multi-plate
capacitors 34 and 36 is related to first multi-plate capacitor 34
functioning primarily as an electrostatic actuator (and secondarily
as a capacitive displacement sensor), and second multi-plate
capacitor 36 functioning as a capacitive displacement sensor. It is
noted that in some instances, first multi-plate capacitor 34 is
referred to as the "electrostatic actuator", and second multi-plate
capacitor 36 is referred to as the "capacitive displacement
sensor", keeping in mind that the electrostatic actuator also
functions as an additional capacitive displacement sensor in some
embodiments.
[0086] FIG. 3 is an exploded-view drawing illustrating one
embodiment of a center plate of a multi-plate capacitor according
to the present invention, such as center plate 38 of first
multi-plate capacitor 34. It is noted that the illustration of FIG.
3 and the following description also applies to center plate 40 of
second multi-plate capacitor 36. In one embodiment, center plate 38
includes a first spring sheet 90, a second spring sheet 92, which
is substantially identical to first spring sheet 90, and a
stabilizer 94. In one embodiment, first and second spring sheets 90
and 92 each have an inner ring 96 supported by a set of three
substantially identical and equally spaced springs 98 which are
coupled to an outer ring 100. In one embodiment, each spring 98
includes an arc shaped first leg 102 following the circumference of
inner ring 96, a turning segment 104, and an arc shaped second leg
106 following the circumference of outer ring 100, with arc shaped
first and second legs 102 and 106 being adjacent to one another. It
is noted that together, springs 98 of first and second spring
sheets 90 and 92 are represented as springs 44 in FIG. 2. First and
second spring sheets 90 and 92 also include a
displaceable-electrode wire tab 108 extending from outer ring 100.
In one embodiment, first and second spring sheets 90 and 92, and
stabilizer 94 are made of beryllium copper.
[0087] In one embodiment, stabilizer 94 includes an inner ring 110
which is initially connected to an outer ring 112 by a set of three
substantially identical and equally spaced temporary connectors
114. In one embodiment, inner ring 110 of stabilizer 94 includes a
set of six substantially identical and equally spaced
weight-reduction holes 116. Initially, as indicated by the vertical
dashed lines in FIG. 3, an inside diameter 120 of inner ring 110 of
stabilizer 94 is smaller than inside diameters 122 of inner rings
96 of first and second spring sheets 90 and 92. Ultimately, the
inside diameters 122 of inner rings 96 of first and second spring
sheets 90 and 92 and inside diameter 120 of inner ring 110 of
stabilizer 94 are enlarged and form a uniform final diameter for
center hole 86 of center plate 38, as illustrated in FIG. 2.
[0088] Center plate 38 is constructed as a stack in the order of
first spring sheet 90, stabilizer 94, and second spring sheet 92.
In one embodiment, inner rings 96 of first and second spring sheets
90 and 92 and inner ring 110 of stabilizer 94 are laminated
together to form displaceable electrode 42. Similarly, outer rings
100 of first and second spring sheets 90 and 92 and outer ring 112
of stabilizer 94 are laminated together to form frame 43. It is
noted that springs 98 of first and second spring sheets 90 and 92
must be kept free of adhesive and form springs 44.
Displaceable-electrode wire tabs 108 of first and second spring
sheets 90 and 92 are wired together to ensure that first and second
spring sheets 90 and 92 are at the same electrical potential. In
one embodiment, as a precaution against introducing a virtual leak
in the high-vacuum environment of a TEM, weight-reduction holes 116
of stabilizer 94 are filled with adhesive during the process of
constructing center plate 38.
[0089] In some instances, construction of center plate 38, as
described above, results in a non-concentric alignment of the
inside diameters 122 of inner rings 96 of first and second spring
sheets 90 and 92 and inside diameter 120 of stabilizer 94. In one
embodiment, using the smaller inside diameter 120 of inner ring 110
of stabilizer 94 as a pilot hole, inside diameters 122 of inner
rings 96 of first and second spring sheets 90 and 92 and inner
diameter 120 of stabilizer 94 are enlarged by drilling to establish
a substantially uniform final diameter of center hole 86 of center
plate 38. After completing the drilling operation, temporary
connectors 114 are removed which frees displaceable electrode 42 to
move as one unit relative to frame 43 when influenced by a force.
The multilayer design of the center plate 38 enables springs 44 to
have a low spring constant simultaneous with displaceable electrode
42 having high flexural rigidity.
[0090] In one embodiment, the spring constant of springs 44 is
optimized relative to the flexural rigidity of displaceable
electrode 42. In one embodiment, the spring constant of springs 44
was optimized with the aid of modeling by finite-element analysis
(FEA). In one embodiment, the finalized design of springs 44
resulted in a nominal modeled spring constant of 197N/m for
actuatable capacitive transducer 30 (each of twelve springs
contributing 16.4N/m). Taking into account dimensional tolerances,
spring constant k of actuatable capacitive transducer 30 is
predicted to fall in the range of 111-345N/m, primarily as a
consequence of a strong dependence on an uncertainty in a thickness
t of the first and second spring sheets 90 and 92
(k.varies.t.sup.3). In one embodiment, actuatable capacitive
transducer 30 was determined to have a measured k of 259N/m,
somewhat higher than a nominal modeled k of 197N/m, but within a
range of possible values. It is noted that the nominal modeled k is
approximately the same as that of Hysitron's three-plate capacitive
transducer, which is comprised of a single three-plate capacitor of
square shape having a total of eight springs of different shape and
dimensions in comparison to springs 44 of actuatable capacitive
transducer 30.
[0091] In one embodiment, FEA was used further to predict whether
springs 44 obeyed Hooke's law when displaceable electrode 42 was
forced to displace up to 5 .mu.m from its natural state in a manner
that only caused a uniform change in the electrode gaps, wherein
"natural state" refers to a positional state of displaceable
electrode 42 when not under the influence of electrostatic and
indenter-sample forces. The FEA results predict excellent adherence
to Hooke's law over this range of displacement, a range easily
large enough for quantitative in-situ TEM nanoindentation because
the depth of electron transparency in a sample is only in the
vicinity of 300 nm for a 300 kV electron beam. FEA was used further
still to predict the largest local strain induced in springs 44
when displaceable electrode 42 was forced to displace 75 .mu.m from
its natural state in the manner described above. This amount of
displacement is equivalent to displaceable electrode 42 of the more
narrowly gapped second multi-plate capacitor 36, in one embodiment,
being forced to contact a neighboring stationary electrode. At 75
.mu.m displacement, the largest local strain in springs 44 is
predicted to be 0.08%, well under the expected elastic strain limit
of 0.2%.
[0092] Returning to FIG. 2, multi-plate capacitor 34 is formed by
adhering first dielectric spacer 74 both to first outer plate 70
and frame 43 of center plate 38, and by adhering second dielectric
spacer 76 both to second outer plate 72 and frame 43 of center
plate 38. Springs 44 and displaceable electrode 42 must be kept
free of adhesive during the joining procedure.
[0093] FIG. 4A is a perspective view representative of one
embodiment of multi-plate capacitor 34 in an assembled condition.
As can be seen in FIG. 4B, assembled multi-plate capacitor 34 is
substantially smaller than a U.S. dime.
[0094] FIG. 5A is an exploded-view drawing further illustrating
actuatable capacitive transducer 30 described by FIGS. 1 through 4A
above. FIG. 5B is a perspective view drawing illustrating
actuatable capacitive transducer 30 in an assembled condition. With
respect to FIG. 5A, dielectric sheath 50 of coupling shaft 46 has a
segment 130 of a major diameter and first and second segments 132
and 134 of a minor diameter, with minor-diameter segment 132 being
longer than minor-diameter segment 134. The minor diameter of first
and second segment 132 and 134 is a tight fit to the drilled-out
uniform final diameter of center holes 86 of center plates 38 and
40 of first and second multi-plate capacitors 34 and 36. The major
diameter of segment 130 is larger than the minor diameter of first
and second segments 132 and 134, but is small enough in comparison
to the diameter of center holes 86 of first and second outer plates
70 and 72 of first and second multi-plate capacitors 34 and 36 to
prevent coupling shaft 46 from contacting the relevant outer plates
after assembly of actuatable capacitive transducer 30.
[0095] With reference to FIG. 5A, the following describes an
example of a sequence of steps for assembling actuatable capacitive
transducer 30. First, pre-assembled first multi-plate capacitor 34
is slipped over longer minor-diameter segment 132 of dielectric
sheath 50, which is pre-adhered to conductive threaded rod 48.
Displaceable electrode 42 of first multi-plate capacitor 34 is then
adhered against a shoulder defined by the transition from longer
minor-diameter segment 132 to major-diameter segment 130 of
dielectric sheath 50. Next, dielectric sleeve 52 is slipped over
longer minor-diameter segment 132 of dielectric sheath 50.
Dielectric sleeve 52 is then adhered to displaceable electrode 42
of first multi-plate capacitor 34 and to dielectric sheath 50, such
that dielectric sleeve 52 does not contact the outer plate through
which it passes. Next, pre-assembled second multi-plate capacitor
36 is slipped over shorter minor-diameter segment 134 of dielectric
sheath 50. Displaceable electrode 42 of second multi-plate
capacitor 36 is then adhered against a shoulder defined by the
transition from shorter minor-diameter segment 134 to
major-diameter segment 130 of dielectric sheath 50. Next,
dielectric standoff 54 is slipped over the unsheathed end of
conductive threaded rod 48 now protruding from second multi-plate
capacitor 36. Dielectric standoff 54 is then adhered to conductive
threaded rod 48 and to displaceable electrode 42 of second
multi-plate capacitor 36, such that dielectric standoff 54 does not
contact the outer plate through which it passes. Next, probe wire
tab 56 is slipped over the unsheathed end of conductive threaded
rod 48 now protruding from dielectric standoff 54, and is retained
by screwing on conductive nut 58. Screwing conductive probe 60 onto
the remaining unsheathed end of conductive threaded rod 48 is
delayed until just prior to use in order to diminish the likelihood
of inadvertently damaging conductive indenter 62.
[0096] With reference to FIG. 5B, conductive transducer body 32 has
a first set of ports 140 and a second set of ports 142 to
facilitate attaching the now mechanically-coupled first and second
multi-plate capacitors 34 and 36 to conductive transducer body 32.
It is noted that not all ports of first and second sets of ports
140 and 142 are visible in the illustration of FIG. 5B. Conductive
transducer body 32 also includes cutouts 144 which will be
described in greater detail below.
[0097] Continuing with the example sequence of steps for assembling
actuatable capacitive transducer 30 described above, the now
mechanically-coupled first and second multi-plate capacitors 34 and
36 are inserted into conductive transducer body 32 such that first
multi-plate capacitor 34 is aligned with first set of ports 140 and
second multi-plate capacitor 36 is approximately aligned with
second set of ports 142. Next, adhesive is injected into first set
of ports 140 to fix first multi-plate capacitor 34 to conductive
transducer body 32.
[0098] Optimum attachment of second multi-plate capacitor 36 to
conductive transducer body 32 requires finely manipulating the
position of second multi-plate capacitor 36 until each or a
specific one of the displaceable electrodes 42 of first and second
multi-plate capacitors 34 and 36 resides, as close as possible,
midway between the corresponding flanking stationary electrodes 80
(see FIG. 2). After achieving the desired condition, adhesive is
injected into second set of ports 142 to fix second multi-plate
capacitor 36 to conductive transducer body 32. In one embodiment,
the method used to maintain the desired distance between first and
second multi-plate capacitors 34 and 36 during adhesive curing
resulted in only a 90 nm deviation from perfectly balancing the
gaps of first multi-plate capacitor 34 (the electrostatic
actuator). One particular nanoindentation operating mode requires
electrostatic actuator 34 having well-balanced electrode gaps.
[0099] Properly fixing the position of second multi-plate capacitor
36 requires this assembly step be done with coupling shaft 46
horizontal in order to match the eventual orientation of actuatable
capacitive transducer 30 in a TEM. If this assembly step is done
with coupling shaft 46 aligned with gravity for example,
displaceable electrodes 42 of first and second multi-plate
capacitors 34 and 36 would end up far from midway between the
flanking stationary electrodes 80 upon reorienting actuatable
capacitive transducer 30 for insertion into a TEM.
[0100] In one embodiment, as can be seen in FIG. 5A, actuatable
capacitive transducer 30 has a central axis 148 about which its
components are predominantly circular in shape, and about which its
components are predominantly concentric. The choice of circular
shapes, rather than square shapes for example, is motivated by
actuatable capacitive transducer 30 being configured to be housed
in a TEM holder. TEM holders, sometimes referred to as TEM rods,
typically posses a tubular geometry. By choosing circular shapes,
the electrode areas can be maximized. Also regarding electrode
areas, displaceable electrodes 42 have a smaller inside diameter
and a larger outside diameter in comparison to stationary
electrodes 80. This intentional mismatch in diameters suppresses a
change in overlapping electrode area in the event displaceable
electrodes 42 are forced to shift sideways with respect to the
stationary electrodes 80.
[0101] As described above, actuatable capacitive transducer 30 must
be oriented with coupling shaft 46 horizontal when operating in a
TEM. A horizontal orientation enables conductive indenter 62 to
intersect the vertically-aligned electron beam of a TEM. As a
consequence of this horizontal orientation, conductive probe 60
will tilt substantially downward if the tilting moment owing to
gravity acting on the mass from conductive indenter 62 to
displaceable electrode 42 of first multi-plate capacitor 34 is not
countered by some means. In addition, conductive indenter 62
contacting a sample having its surface slanted relative to central
axis 148 of actuatable capacitive transducer 30 will cause a net
sideways force, thereby introducing an additional tilting moment.
On account of TEM design, the distance from conductive indenter 62
to displaceable electrode 42 of first multi-plate capacitor 34
cannot be significantly shortened to substantially reduce these
tilting moments.
[0102] Countering tilting moments is a major impetus for employing
second multi-plate capacitor 36. By separating the first and second
multi-plate capacitors 34 and 36 by a significant fraction of the
distance from conductive indenter 62 to displaceable electrode 42
of first multi-plate capacitor 34, the tendency to tilt is greatly
reduced. However, there is a compromise between lengthening the
portion of coupling shaft 46 between displaceable electrodes 42 of
the first and second multi-plate capacitors 34 and 36 and
preserving a high mechanical natural frequency, because the mass of
coupling shaft 46 is the dominant mass carried by the springs
44.
[0103] The following Expression E.1 can be used to calculate the
mechanical natural frequency v.sub.o of a spring-mass system:
v o = 1 2 .pi. k m ; E .1 ##EQU00001##
where k retains the meaning defined above and m is the sprung mass
of actuatable capacitive transducer 30. In one embodiment of
actuatable capacitive transducer 30, v.sub.o was measured to be 133
Hz with conductive probe 60 attached, which yielded 372 mg for m
given the measured k of 259N/m. The measured v.sub.o of actuatable
capacitive transducer 30 is comparable to what generally is found
for Hysitron's three-plate capacitive transducer equipped with its
probe, which is not electrically conductive.
[0104] FIG. 6 is a diagram illustrating aspects of the electrical
configuration of actuatable capacitive transducer 30. As
illustrated by FIG. 6, the electrostatic actuator (i.e., first
multi-plate capacitor 34) has a different electrical configuration
compared to the capacitive displacement sensor (i.e., second
multi-plate capacitor 36). Signals inputted to electrostatic
actuator 34 include V.sub.1+V.sub.m, as indicated at 150, to the
one of stationary electrodes 80 of electrostatic actuator 34
closest to conductive indenter 62, and V.sub.2-V.sub.m, as
indicated at 152, to the other stationary electrode 80 of the
electrostatic actuator 34. Signals inputted to the capacitive
displacement sensor include +V.sub.m to the capacitive displacement
sensor's stationary electrode closest to the conductive indenter
and -V.sub.m to the other stationary electrode of the capacitive
displacement sensor.
[0105] Input signals V.sub.1 and V.sub.2 are electrostatic
actuation voltages, while input signals +V.sub.m and -V.sub.m,
indicated at 154 and 156, are high-frequency modulation voltages
equal in frequency, waveform, and amplitude but different in phase
by 180.degree.. The frequency of +V.sub.m and -V.sub.m is much
higher than v.sub.o; therefore, actuatable capacitive transducer 30
does not mechanically respond to these input signals. In one
embodiment of a built actuatable capacitive transducer 30, both
+V.sub.m and -V.sub.m are 130 kHz square waves with an amplitude of
10V peak-to-peak, and both V.sub.1 and V.sub.2 cover the range of
0-600V. Displaceable electrode 42 of electrostatic actuator 34 is
effectively at ground relative to V.sub.1 and V.sub.2.
[0106] Electrostatic actuator 34 outputs a V.sub.out1 signal, as
indicated at 158, from corresponding displaceable electrode 42.
Capacitive displacement sensor 36 outputs a V.sub.out2 signal, as
indicated at 160, from corresponding displaceable electrode 42. The
frequency and the waveform of +V.sub.m and -V.sub.m dictate the
frequency and the waveform of V.sub.out1 158 and V.sub.out2 160. In
a fashion similar to Hysitron's three-plate capacitive transducer
and to the IFM sensor, both electrostatic actuator 34 and
capacitive displacement sensor 36 are electrically configured to
execute the well-established differential capacitance half-bridge
method of displacement detection.
[0107] With the differential capacitance half-bridge method, an
output signal V.sub.out of an appropriately configured multi-plate
capacitor (specifically an appropriately configured three-plate
capacitor) is ideally given by the following Expression E.2:
v out = C 1 - C 2 C 1 + C 2 V m ; E .2 ##EQU00002##
where C.sub.1 is the capacitance between displaceable electrode 42
and one neighboring stationary electrode 80, C.sub.2 is the
capacitance between displaceable electrode 42 and the other
neighboring stationary electrode 80, and |V.sub.m| is the amplitude
of either +V.sub.m or -V.sub.m. Output signal V.sub.out can be of
either sign depending on which of C.sub.1 and C.sub.2 is larger.
The amplitude of V.sub.out is zero when C.sub.1=C.sub.2, and is
|V.sub.m| when displaceable electrode 42 is in contact with either
neighboring stationary electrode 80. Expression E.2 applies both to
V.sub.out1 and V.sub.out2. The differential capacitance half-bridge
method has the characteristic of being relatively insensitive to
tilting of displaceable electrodes 42 relative to stationary
electrodes 80 and, thus, to vibrations that induce oscillatory
tilting. This is particularly important, because actuatable
capacitive transducer 30 is most susceptible to vibrations that
induce oscillatory tilting on account of its horizontal orientation
in a TEM.
[0108] In terms of geometric parameters, the capacitance C of a
parallel-plate capacitor is given by Expression E.3 below:
C = o A d ; E .3 ##EQU00003##
where .di-elect cons..sub.o is the electrical permittivity constant
(8.85.times.10.sup.-12 F/m), A is the overlapping electrode area,
and d is the electrode gap. Expression E.3 can be used to calculate
either multi-plate capacitor's nominal capacitance, i.e., the value
of C.sub.1 or C.sub.2 for the state in which C.sub.1=C.sub.2 which
ideally corresponds to balanced electrode gaps. In one embodiment,
the nominal capacitance of electrostatic actuator 34 is calculated
to be 0.80 pF, assuming d'.sub.1=d'.sub.2=100 .mu.m and A=9.03
mm.sup.2, where d'.sub.1 and d'.sub.2 are electrode gaps 162 and
164 of electrostatic actuator 34. In one embodiment, the nominal
capacitance of capacitive displacement sensor 36 is calculated to
be 1.1 pF, assuming d.sub.1=d.sub.2=75 .mu.m and A=9.03 mm.sup.2,
where d.sub.1 and d.sub.2 are electrode gaps 166 and 168 of
capacitive displacement sensor 36. In one embodiment, actuatable
capacitive transducer 30 is designed such that A is single valued.
A nominal capacitance of 1 pF is the rule-of-thumb cutoff for good
design practice; therefore, actuatable capacitive transducer 30 is
configured to be in the vicinity of the rule-of-thumb cutoff.
[0109] Replacing C.sub.1 and C.sub.2 in E.2 with
o A d 1 and o A d 2 , ##EQU00004##
respectively, results in the following Expression E.4 for
capacitive displacement sensor 36:
V out 2 = d 2 - d 1 d 2 + d 1 V m = .DELTA. d d _ V m ; E .4
##EQU00005##
where d is the constant mean of d.sub.1 and d.sub.2, and where
.DELTA.d (which can be of either sign) is the change in one
electrode gap (e.g., the change in d.sub.2) relative to the
condition in which the electrode gaps are balanced
(d.sub.1=d.sub.2= d). The change in the other electrode gap (e.g.,
the change in d.sub.1) relative to the balanced condition is
identical in magnitude but opposite in sign. A small d is conducive
to high displacement sensitivity, which is the reason, in one
embodiment, for utilizing thinner dielectric spacers 74 and 76 for
capacitive displacement sensor 36 relative to electrostatic
actuator 34. Expression E.4 predicts V.sub.out2 to be a perfectly
linear function of .DELTA.d over the entire range of displacement.
But in practice, parasitic capacitance not dependent on
.DELTA. d d _ ##EQU00006##
restricts satisfactory linearity to some range less than the full
range about the balanced condition. In one embodiment, both first
and second multi-plate capacitors 34 and 36 of actuatable
capacitive transducer 30 (an equation analogous to E.4 is
applicable to the displacement sensing function of electrostatic
actuator 34) are satisfactorily linear over a displacement range of
.+-.5 .mu.m about the natural state of displaceable electrodes 42.
Larger displacements have not been experimentally investigated as
they are not necessary for quantitative in-situ TEM
nanoindentation.
[0110] Focusing now on electrostatic actuation, the electrostatic
force F.sub.e generated by a parallel-plate capacitor comprised of
a displaceable electrode and a stationary electrode is given by the
following Expression E.5:
F e = .kappa. o ( 1 - .delta. / d o ) V 2 ; E .5 ##EQU00007##
where V is the electrostatic actuation voltage across the two
electrodes, d.sub.o is the electrode gap when V=0, .delta. is the
displaceable electrode displacement from d.sub.o, and where the
electrostatic force constant .kappa..sub.o is given by Expression
E.6 below:
.kappa. o = o A 2 d o 2 ; E .6 ##EQU00008##
where .di-elect cons..sub.o and A retain their previously expressed
definitions. In general, .delta. can be of either sign depending on
the nature of the force displacing the displaceable electrode;
however, F.sub.e can only cause the displaceable electrode to be
attracted to the stationary electrode on account of its V.sup.2
dependence.
[0111] Assume V in E.5 corresponds to V.sub.1 and that V.sub.2=0.
Also assume that conductive probe 60 is sufficiently blocked from
moving so that .delta.=0 always. Setting d.sub.o equal to a chosen
100 .mu.m thickness of dielectric spacers 74 and 76 of
electrostatic actuator 34 results in actuatable capacitive
transducer 30 having an expected .kappa..sub.o of 4.0 nN/V.sup.2
and an expected maximum blocked F.sub.e of 1.4 mN at V.sub.1's
maximum of 600V. In one embodiment, the electrostatic force
constant .kappa..sub.o and the maximum blocked F.sub.e of a built
actuatable capacitive transducer 30 were determined to be 3.6
nN/V.sup.2 and 1.3 mN, respectively, both reasonably close to
expectation. The capacity to generate a maximum blocked F.sub.e in
the vicinity of 1 mN is a good compromise between achieving high
resolution in F.sub.e and generating enough F.sub.e to indent a
wide variety of samples up to their maximum depth of electron
transparency, which is the reason for utilizing thicker dielectric
spacers 74 and 76 for electrostatic actuator 34 relative to
capacitive displacement sensor 36 in one embodiment.
[0112] In reality, .delta. is permitted to change. Displacement of
displaceable electrode 42 must be assumed to be increasingly
positive when conductive probe 60 moves toward a sample in order to
be compatible with expression E.5 above. A changing .delta. affects
the scaling between F.sub.e and V.sup.2 through the denominator of
expression E.5, the scaling being increasingly enhanced when
.delta. becomes increasingly positive and being increasingly
diminished when .delta. becomes increasingly negative. In most
instances, V.sub.2 remains at zero while V.sub.1 is being varied
during the nanoindentation test, but V.sub.2 being connected
provides a benefit nonetheless. Often, the dominant contributor of
noise to V.sub.1 and V.sub.2 is found to be in-phase AC line noise;
therefore, the electrostatic force noise associated with AC line
noise present on V.sub.2 tends to cancel the electrostatic force
noise associated with AC line noise of the same phase present on
V.sub.1.
[0113] Still assuming V.sub.2=0, F.sub.e represents a total applied
force (always positive if non-zero) equal to the contact force
F.sub.e (positive if repulsive to adhere to convention) plus the
spring force F.sub.s=k.delta. (the customary minus sign is dropped
for convenience), which is a consequence of the parallel loading
configuration. Hence, the following Expression E.7 can be used to
calculate the contact force:
F.sub.c=F.sub.e-k.delta. E.7.
Expression E.7 also applies to actuation with conductive indenter
62 far from a sample. In that case, F.sub.c=0 and
F.sub.e=k.delta..
[0114] The snap-to-contact instability and the spark-gap
instability must be kept in mind when actuating electrostatically.
To simplify the following discussion, again assume V.sub.2=0. The
snap-to-contact instability refers to displaceable electrodes 42
suddenly snapping toward the electrostatic actuator's stationary
electrode 80 with V.sub.1 applied. The possibility of this
happening can be deduced from electrostatic force gradient vs.
spring constant considerations, and is predicted to occur when
d.sub.1 narrows to 2/3d.sub.o (or equivalently when
.delta.=1/3d.sub.o) if the resistance to motion obeys Hooke's law;
a higher order resistance to motion retards this instability. The
spark-gap instability refers to a spark crossing d.sub.1 when the
electric field strength given by the ratio of V.sub.1 to d.sub.1
exceeds a critical value, which has the highest likelihood when the
snap-to-contact instability is reached, but which can happen even
prior to reaching the snap-to-contact instability. The critical
electric field strength depends on pressure and has the lowest
value in the corona discharge region in the vicinity of
10.sup.-2-10.sup.-3 torr; therefore, actuatable capacitive
transducer 30 should not be actuated while pumping down to the
.about.10.sup.-7 torr operating pressure of a TEM. Fortunately, the
spark-gap instability is of much reduced concern at
.about.10.sup.-7 torr. The instrument's software limits .delta. to
5 .mu.m to ensure the snap-to-contact instability and the spark-gap
instability never occurring.
[0115] Drive cards ordinarily used for Hysitron's three-plate
capacitive transducers facilitate the electrical configurations of
the first and second multi-plate capacitors 34 and 36 of actuatable
capacitive transducer 30 and the following describes their
employment in one embodiment. Electrostatic actuator 34 is
electrically connected to a first drive card and capacitive
displacement sensor 36 is electrically connected to a second drive
card, the first and second drive cards being identical in design
but different in implementation. Each of the first and second drive
cards (one can be seen in the photograph of FIG. 4B) generates
+V.sub.m and -V.sub.m and has the capacity for coupling
electrostatic actuation voltages to these high-frequency modulation
signals. The first drive card for electrostatic actuator 34 couples
V.sub.1 and V.sub.2 supplied by a transducer controller to +V.sub.m
and -V.sub.m generated by this drive card in the manner described
above. The second drive card for capacitive displacement sensor 36
simply couples a ground signal supplied by the transducer
controller to +V.sub.m and -V.sub.m generated by this drive card to
disable electrostatic actuation.
[0116] Each of the first and second drive cards has a preamplifier
having high input impedance and low output impedance. Each of the
first and second drive cards also has circuitry for synchronous
demodulation of the preamplifier's output as well as circuitry for
subsequent low-pass filtering of the synchronous demodulator's
output to generate a useful displacement signal. The first drive
card's preamplifier receives V.sub.out1 from electrostatic actuator
34. The second drive card's preamplifier receives V.sub.out2 from
capacitive displacement sensor 36. The first drive card ultimately
outputs V.sub.disp1 to the transducer controller for amplification
and filtering beyond what is provided by this drive card,
V.sub.disp1 being its useful displacement signal. The second drive
card ultimately outputs V.sub.disp2 to the transducer controller
for amplification and filtering beyond what is provided by this
drive card, V.sub.disp2 being its useful displacement signal. In
general, V.sub.disp1.noteq.V.sub.disp2 but both represent .delta.
if properly calibrated, e.g., via measurement of V.sub.disp1 and
V.sub.disp2 vs. the displacement readout of an interferometer. In
one embodiment, invoking a single modulation frequency of 130 kHz
did not cause detectable coupling between V.sub.disp1 and
V.sub.disp2. Separating the modulation frequency of the first drive
card from that of the second drive card by several times the
roll-off frequency of the post-demodulation low-pass filters can be
employed to suppress coupling between V.sub.disp1 and V.sub.disp2
if problematic.
[0117] Points available on first and second multi-plate capacitors
34 and 36 for wire soldering are illustrated in FIG. 4A. Wires from
the drive cards that carry the signals to be inputted to stationary
electrodes 80 are soldered to stationary-electrode wire pads 170.
Wires to the drive cards that carry the signals being outputted by
displaceable electrodes 42 are soldered to displaceable-electrode
wire tabs 108. Wires from the drive cards that carry the ground
signal are soldered to the ground planes 84 of first and second
multi-plate capacitors 34 and 36 and also to the conductive
transducer body 32; these grounded elements serve as electrical
shields. Wires from the drive cards that carry guard signals are
soldered to guard-ring wire pads 172 (see FIG. 4A). The guard
signal of electrostatic actuator 34 corresponds to the output of
the first drive card's preamplifier, with both guard rings 82 of
electrostatic actuator 34 receiving this guard signal. The guard
signal of capacitive displacement sensor 36 corresponds to the
output of the second drive card's preamplifier, with both guard
rings 82 of capacitive displacement sensor 36 receiving this guard
signal. The purpose is to guard the easily loaded signals present
on displaceable electrodes 42. Perimeter holes 174, as shown in
FIG. 4A facilitate wire routing. Cutouts 144 in conductive
transducer body 32, as illustrated in FIG. 5B provide access to the
soldering points after assembly of actuatable capacitive transducer
30, and also serve as venting for the purpose of evacuating air in
a TEM.
[0118] Ordinarily, it is desirable to position the drive cards in
very close proximity to the corresponding one of the first and
second multi-plate capacitors 34 and 36 to minimize the length of
wiring carrying the easily loaded signals being outputted by
displaceable electrodes 42. However, placing the drive cards in
high vacuum raises considerable thermal management and outgassing
load issues. Consequently, the drive cards reside in the posterior
of the TEM holder that remains at atmospheric pressure and results
in a distance of approximately 1 ft between the drive cards and
actuatable capacitive transducer 30 located at the anterior of the
TEM holder Vacuum-compatible electrical feedthroughs facilitate the
passage of wiring from atmospheric pressure into high vacuum. In
spite of long wiring runs, actuatable capacitive transducer 30
performs well in a TEM through use of cabling having minimal
capacitance between its conductors and its grounded shield.
Moreover, the drive cards and the cabling are held such that they
move with actuatable capacitive transducer 30 whenever actuatable
capacitive transducer 30 is translated relative to the TEM holder.
This avoids a change in electrical layout that might change the
amount of capacitance between the conductors and the grounded
shield of the cabling. Guarding rather than shielding the
conductors carrying the signals being outputted by displaceable
electrodes 42 has not been examined since guarding complicates the
design of the cabling.
[0119] All materials associated with the actuatable capacitive
transducer 30, including the adhesives (specialty epoxies), the
materials of the cabling (copper, Teflon.RTM., and brass), and the
solder (silver), are sufficiently low in outgassing rate to be
compatible with high vacuum. Furthermore, these materials are
sufficiently low in ferromagnetic content to not cause undue
difficulty when subjected to a strong magnetic field. Compatibility
with these aspects of a TEM also means materials compatibility with
a scanning electron microscope (SEM) for quantitative in-situ SEM
nanoindentation. Although not yet verified, the built actuatable
capacitive transducer is potentially compatible with use in
ultra-high vacuum. Obviously, the materials of the built actuatable
capacitive transducer are compatible with use in air or inert gas
environments as well.
[0120] FIG. 7 is a photograph illustrating one embodiment of a
nanoindentation head 180 according to the invention. As illustrated
in FIG. 7, a nanoindentation head 180 comprises actuatable
capacitive transducer 30 mechanically coupled to a 3D piezoelectric
actuator 182. The 3D piezoelectric actuator 182 includes a
one-piece piezoelectric (piezo) tube 184 comprised of an x-y
segment 186 and a z segment 188; and has a hollow interior that
serves as a conduit for the wiring to actuatable capacitive
transducer 30. The z segment 188 is defined by an outer electrode
(denoted z.sub.outer) and an inner electrode (denoted z.sub.inner)
sandwiching the piezoelectric material. The x-y segment 186 is
defined by four outer electrodes (denoted +x.sub.outer,
-x.sub.outer, +y.sub.outer, and -y.sub.outer) and four inner
electrodes (denoted +x.sub.inner, -x.sub.inner, +y.sub.inner, and
-y.sub.inner) sandwiching the piezoelectric material. Voltages
applied differentially to z.sub.outer and z.sub.inner will induce z
segment 188 to extend or contract, thereby displacing actuatable
capacitive transducer 30 along z axis 190 depicted in FIG. 7. A
voltage applied to +x.sub.outer and -x.sub.inner and a voltage of
the same magnitude but of opposite polarity applied to -x.sub.outer
and +x.sub.inner will induce x-y segment 186 to bend, thereby
displacing actuatable capacitive transducer 30 principally along
the x axis, which is orthogonal to the z axis 190. Displacing
actuatable capacitive transducer 30 principally along the y axis,
which is orthogonal to the x and z axes involves an analogous
application of voltages to the y electrodes.
[0121] In one embodiment, 3D piezoelectric actuator 182 of
nanoindentation head 180 is made of a hard lead zirconate titanate
(PZT) ceramic, where "hard" refers to a small d.sub.31
piezoelectric constant, and its electrodes are of silver rather
than of customary nickel to avoid nickel's ferromagnetism. Driven
by a piezo controller capable of outputting differential voltages
ranging from +370V to -370V, 3D piezoelectric actuator 182 of
nanoindentation head 180 is capable of displacing actuatable
capacitive transducer 30 .+-.55 .mu.m along the x and y axes and
.+-.4.7 .mu.m along the z axis 190. The 3D piezoelectric actuator
182 is employed primarily as a sub-nm-resolution positioner, but it
also participates in certain nanoindentation operating modes, and
it can be used to raster scan the conductive indenter 62 to image a
sample's surface in the manner of an AFM if desired. Although 3D
piezoelectric actuator 182 currently does not employ a displacement
sensor dedicated to measuring the extension or the contraction of z
segment 188, the choice of a hard PZT ceramic helps to improve the
reliability of correlating the motion provided to the differential
voltage applied.
[0122] Nanoindentation head 180 is designed to be housed in a
newly-developed TEM holder based largely on earlier TEM holders
developed at National Center for Electron Microscopy/Lawrence
Berkeley National Laboratory (NCEM/LBNL) for qualitative and
semi-quantitative in-situ TEM nanoindentation (see References 6-11
and 13-17). Nevertheless, a TEM holder according to the present
invention, as will be described in greater detail below,
substantially outperforms these prior-art in-situ TEM
nanoindentation holders, particularly with respect to load frame
stiffness and coarse positioning stability, the latter aspect being
related to the former aspect. In fact, Reference 10 and the
erroneously titled Reference 9 pertain to taking advantage of poor
load frame stiffness to deduce the contact force.
[0123] FIG. 8A is a photograph illustrating one embodiment of a TEM
holder 200 according to the present invention. FIG. 8B is a
photograph illustrating a tongue portion 202 of TEM holder 200.
FIG. 8C is a photograph illustrating TEM holder 200 inserted into a
TEM 203 with its posterior 204 visible. It is noted that TEM 203
illustrated in FIG. 8C comprises a JEOL JEM 3010 TEM. With
reference to FIG. 7, nanoindentation head 180 includes an internal
tube 206 which mechanically supports nanoindentation head 180.
Internal tube 206 is internal to an external tube 208, which is
illustrated in FIG. 8A. Also illustrated in FIG. 8A are three
coarse positioning screws 210. Manually turning the three coarse
positioning screws 210 causes the internal tube 206 to be
positioned three dimensionally with respect to external tube 208,
thereby causing the nanoindentation head 180 to be positioned three
dimensionally with respect to tongue 202, which is most easily seen
in FIG. 8B. In one embodiment, the resolution of coarse positioning
is 200 .mu.m/rev. In one embodiment, as illustrated by FIG. 8B,
tongue 202 includes a sample clamp 212 to tightly hold a
wedge-shaped sample, such as the one depicted in FIG. 11A below and
illustrated as being indented by conductive indenter 62. Sample
clamp 212 is easily detached from TEM holder 200 to facilitate
screwing of conductive probe 60 on or off the portion of conductive
threaded rod 48 protruding from coupling shaft 46 of actuatable
capacitive transducer 30. Tongue 202 is the portion of TEM holder
200 that inserts into the narrow pole piece gap of a TEM. All
objects penetrating tongue 202 must be confined to the dimensions
of the tongue.
[0124] It is desirable to keep the sample stationary, especially
when invoking nanoindentation operating modes involving 3D
piezoelectric actuator 182 to affect the indenter-sample
separation. Keeping the sample stationary enables the sample's
region of interest to fully fill the TEM's field of view and
eliminates the possibility of a portion of the sample's region of
interest shifting out of the TEM's field of view during
nanoindentation tests involving 3D piezoelectric actuator 182. In
contrast, Nanofactory's instrument keeps its miniature two-plate
capacitive transducer stationary while actuating its piezoelectric
actuator carrying the sample to affect the indenter-sample
separation (see Reference 20).
[0125] FIG. 9 is a block diagram illustrating generally one
embodiment of a control system 220 for nanoindentation head 180
according to the present invention. Control system 220 is comprised
of a transducer controller 222 (as mentioned above), a piezo
controller 224 (as mentioned above), a digital signal processor
(DSP) based controller 226 capable of 100 million instructions per
second, and a computer 228 running the instrument's software.
Computer 228 is in communication with DSP controller 226 via a
universal serial bus (USB) link 230. In one embodiment, computer
228 comprises a laptop computer. DSP controller 226 is in
communication with transducer controller 222, which is cabled, as
indicated at 232, to the drive cards of actuatable capacitive
transducer 30 housed within the TEM holder 200, and with piezo
controller 224, which is cabled, as indicated at 234, to 3D
piezoelectric actuator 182 also housed within TEM holder 200. In
one embodiment, transducer controller 222 and piezo controller 224
are based, in part, on units currently supplied with Hysitron's
suite of nanoindenters. As a result, control system 220 is an
enabler of imaging in the manner of an AFM in addition to being an
enabler of nanoindentation tests. DSP controller 226, on the other
hand, is an entirely new development.
[0126] DSP controller 226 is programmable and has a memory space
236 for storing instructions received from computer 228, and a
memory space 238 for storing digitized data to be received by
computer 228. DSP controller 226 also includes a plurality of
16-bit digital-to-analog converters (DACs) 240, a plurality of
16-bit analog-to-digital converters (ADCs) 242, a plurality of
programmable gain amplifiers (PGAs) 244, a plurality of voltage
attenuators (VAs) 246, and a plurality of digital input-output
channels (DIOs) 248 to carry out its various programmed tasks. DACs
240 generate analog voltages which are amplified by PGAs 244. The
outputs of the PGAs are further amplified either by transducer
controller 222 to generate V.sub.1 and V.sub.2 to actuatable
capacitive transducer 30 via the first drive card or by piezo
controller 224 to generate the voltages to 3D piezoelectric
actuator 182. ADCs 242 digitize analog voltages outputted by VAs
246, which receive certain analog signals to attenuate before
digitization, including V.sub.disp1 and V.sub.disp2 as provided by
transducer controller 222. The necessity of PGAs 244 and VAs 246 is
linked to a mismatch in DAC 240 and ADC 242 saturation levels in
comparison to transducer controller 222 and piezo controller 224
saturation levels. DIOs 248 are used to control chip states of
various chips included in transducer controller 222, piezo
controller 224, and DSP controller 226. DSP controller 226
generally executes control loops at a 22 kHz loop rate but can
execute control loops at loop rates as high as 80 kHz. Several
control loops provide the characteristic of active damping, a
particularly important characteristic to provide when actuatable
capacitive transducer 30 is operating in the extremely low damping
environment of a TEM.
[0127] DSP controller 226 enables a variety of nanoindentation
operating modes which represent methods of conducting quantitative
in-situ TEM nanoindentation providing that a stream of TEM images
that show how the sample deforms while being indented is
viewed/recorded. The following is a list of at least six
nanoindentation operating modes capable of being performed by
control system 220: [0128] 1. Load control mode--utilize either a
feedback control algorithm (e.g., proportional-integral-derivative
or PID) or a feedforward augmented feedback control algorithm with
optionally adaptive characteristics to adjust V.sub.1 (V.sub.2=0)
in a manner that causes the contact force to meet a predetermined
contact force vs. time function while keeping 3D piezoelectric
actuator 182 static. The development of this mode for Hysitron's
three-plate capacitive transducer has been described in Reference
4. [0129] 2. Displacement control mode--utilize either a feedback
control algorithm or a feedforward augmented feedback control
algorithm with optionally adaptive characteristics to adjust
V.sub.1 (V.sub.2=0) in a manner that causes the indenter
displacement to meet a predetermined indenter displacement vs. time
function while keeping 3D piezoelectric actuator 182 static. The
development of this mode for Hysitron's three-plate capacitive
transducer also has been described in Reference 4. [0130] 3.
Single-sided force-feedback control mode (another form of
displacement control)--conduct single-sided force-feedback control
involving fed-back adjustments to V.sub.1 (V.sub.2=0) while varying
the differential voltage to the z segment 188 of 3D piezoelectric
actuator 182 to affect the indenter-sample separation. This mode is
analogous to the torque balance operation of the IFM in the sense
that displaceable electrodes 42 are suppressed from deflecting.
[0131] 4. Double-sided force-feedback control mode (vet another
form of displacement control)--conduct double-sided force-feedback
control involving coordinated fed-back adjustments to V.sub.1 and
V.sub.2 while varying the differential voltage to the z segment 188
of 3D piezoelectric actuator 182 to affect the indenter-sample
separation. This mode also is analogous to the torque balance
operation of the IFM in the sense just mentioned. However, this
mode in conjunction with actuatable capacitive transducer 30 has a
certain novel advantage over the torque balance operation of the
IFM, which will be explained in greater detail below. [0132] 5.
Open-loop mode (an open-loop approximation of load control)--vary
V.sub.1 (V.sub.2=0) in an open-loop manner in accordance with a
predetermined blocked electrostatic force vs. time function while
keeping 3D piezoelectric actuator 182 static. This is the
traditional nanoindentation operating mode of Hysitron's
three-plate capacitive transducer. [0133] 6. Spring-force mode--do
not actuate the electrostatic actuator 34 (V.sub.1=V.sub.2=0) and
measure the spring force that relates to the contact force while
varying the differential voltage to the z segment 188 of 3D
piezoelectric actuator 182 to affect the indenter-sample
separation. Disconnecting the electrostatic actuation circuitry
from electrostatic actuator 34 before executing this mode will
eliminate spring force noise derived from electrostatic force
noise. This mode is reminiscent of an AFM or Nanofactory's
instrument attempting to conduct nanoindentation.
[0134] The following assumes that the relevant electrostatic force
constant is calibrated rather than calculated from geometric
parameters. Nanoindentation operating modes numbered 1, 2, and 5 in
the above list require knowledge of .kappa..sub.o, d.sub.o, and k
to calculate F.sub.c because displaceable electrodes 42 are
displaced during the nanoindentation test (see Expression E.7 in
conjunction with Expression E.5). Mode number 3 from the above list
requires knowledge of .kappa..sub.o and d.sub.o to calculate
F.sub.c, but not k because displaceable electrodes 42 are
suppressed from displacing during the nanoindentation test. The not
obvious necessity of knowing both .kappa..sub.o and d.sub.o in the
case of mode numbered 3 will be explained in greater detail below.
Mode number 4 from the above list requires knowledge of a K.sub.b
corresponding to the electrostatic force constant for the balanced
condition to calculate F.sub.c, but not k or d (the balanced
condition's analog to d.sub.o) because displaceable electrodes 42
are suppressed from displacing during the nanoindentation test; a
contact force equation utilizing .kappa..sub.b will be provided in
the next paragraph. Mode number 6 from the above list does not
require knowledge of .kappa..sub.o or d.sub.o because this mode
does not involve generation of electrostatic force, but obviously
requires the knowledge of k to calculate F.sub.c. Of course, the
above list is not exhaustive. For example, it is also possible to
invoke modes involving variations in V.sub.1 and V.sub.2 that cause
.delta. to change while keeping 3D piezoelectric actuator 182
static, but such modes are more complicated to calibrate than the
others.
[0135] The following begins a detailed explanation of the novel
advantages of the double-sided force-feedback control mode over the
torque balance operation of the IFM. First, assume electrostatic
actuator 34 is endowed with perfectly balanced electrode gaps at
V.sub.1=V.sub.2=0 when conductive indenter 62 is far removed from
the sample. Next, assume the electrode gaps of electrostatic
actuator 34 remain balanced after equating both V.sub.1 and V.sub.2
to a bias voltage V.sub.o (preferably 300V), conductive indenter 62
still being far removed from the sample. Additionally, assume
V.sub.1=V.sub.o+V.sub.fb and V.sub.2=V.sub.o-V.sub.fb when using
this nanoindentation operating mode, where V.sub.fb is a fed-back
adjustment to V.sub.1 and V.sub.2, which is restricted to the range
of .+-.V.sub.o, and which keeps the electrode gaps of electrostatic
actuator 34 balanced in the presence of F.sub.c. With this
scenario, V.sub.fb is zero when conductive indenter 62 is far
removed from the sample, and is negative or positive when F.sub.c
is attractive or repulsive, respectively. Setting the sum of the
electrostatic force owing to V.sub.1, the electrostatic force owing
to V.sub.2, and F.sub.c to zero yields the following Expression E.8
for the contact force:
F.sub.c=4.kappa..sub.bV.sub.oV.sub.fb E.8;
which means F.sub.c is a linear function of V.sub.fb. In practice,
achieving a high degree of linearity requires maintaining the
electrode gaps of electrostatic actuator 34 (rather than the
electrode gaps of capacitive displacement sensor 36) at the
balanced condition, which is the motivation for utilizing
electrostatic actuator 34 as an additional capacitive displacement
sensor.
[0136] The following continues the detailed explanation of the
novel advantages of the double-sided force-feedback control mode
over the torque balance operation of the IFM. In the case of the
IFM, it is the sum of the torques rather than of the forces that is
directly pinned to zero by the action of the
electrostatic-force-feedback controller. Keeping this in mind,
let's examine the IFM sensor being controlled in a manner analogous
to the double-sided force-feedback control mode of the present
invention. With this assumption, setting the sum of the torques to
zero (again assuming inherently balanced electrode gaps) yields
Expression E.9 below:
F.sub.c=4.kappa..sub.bV.sub.oV.sub.fbL/L' E.9;
where L is the moment arm from either electrostatic force to the
torsion bar axis and L' is the moment arm from the indenter to the
torsion bar axis. Hence, the IFM also is capable of operating in a
manner in which F.sub.c is a linear function of V.sub.fb. However,
achieving linearity comes with a difficulty: the sum of the
indenter-side electrostatic force
.kappa..sub.b(V.sub.o-V.sub.fb).sup.2, the non-indenter-side
electrostatic force .kappa..sub.b(V.sub.o+V.sub.fb).sup.2, and
F.sub.c is not kept at the initial sum of these forces equaling
2.kappa..sub.bV.sub.o.sup.2. In fact, the change in the sum of
these forces relative to 2.kappa..sub.bV.sub.o.sup.2 is given by
F.sub.c+2.kappa..sub.bV.sub.fb.sup.2 which clearly is nonzero in
general. As a consequence, the torsion bars will deflect in a
manner resulting in the electrode gaps uniformly expanding or
collapsing, with the amount of this unintended deflection being
dictated by the associated restoring force of the torsion bars
equilibrating with the change in the sum of the electrostatic
forces and F.sub.c. The electrode gaps expanding or collapsing
uniformly results in an atypical mechanical compliance not directly
detectable by the IFM, and introduces error in the calculation of
F.sub.c because Expression E.9 assumes the electrode gaps to be
invariant.
[0137] The following concludes the detailed explanation of the
novel advantages of the double-sided force-feedback control mode
over the torque balance operation of the IFM. As it turns out, the
only way of eliminating the atypical source of mechanical
compliance is to fix the non-indenter-side electrostatic force to
.kappa..sub.bV.sub.o.sup.2 and set L and L' to be equal. With this
configuration, Expression E.10 yields:
F.sub.c=2.kappa..sub.bV.sub.oV.sub.fb-.kappa..sub.bV.sub.fb.sup.2
E.10;
which means F.sub.c is no longer a linear function of V.sub.fb.
Obviously, the double-side force-feedback control mode in
combination with actuatable capacitive transducer 30 (or in
combination with any other nanoindentation transducer comprising a
stacked three-plate electrostatic actuator, such as Hysitron's
three-plate capacitive transducer, for example) is an improvement
over any form of torque balance operation of the IFM.
[0138] The wide variety of nanoindentation operating modes feasible
for use with control system 220 of nanoindentation head 180 are not
equally worthy when conducting nanoindentation tests in a TEM.
Reference 4 describes the overwhelming superiority of displacement
control over load control if the goal is to investigate discrete
deformation phenomena such as the onset of plasticity, likely an
impetus for quantitative in-situ TEM nanoindentation
experimentation. Furthermore, displacement control rather than load
control provides nanoindentation data that can be directly compared
to molecular dynamics simulations and finite element modeling of
nanoindentation-induced deformation, also likely an impetus for
quantitative in-situ TEM nanoindentation experimentation. Modes
numbered 2-4 in the above list are variations of displacement
control, but those numbered 3 and 4 require an additional
displacement sensor dedicated to measuring the extension or
contraction of 3D piezoelectric actuator 182 to achieve high
penetration depth accuracy. Consequently, mode numbered 2
represents the simplest path to quantitative
displacement-controlled force-displacement curves. However, modes
numbered 3 and 4 are superior from the viewpoint of transducer
control performance because it is easier to simply fend off forces
attempting to deflect displaceable electrodes 42 in comparison to
meeting an indenter displacement demand ramp, as is the case with
mode number 2. Mode number 3 does require V.sub.1>0 before
engaging a sample in order to have a range of V.sub.1 in reserve
for fending off attractive forces acting on conductive indenter
62.
[0139] Mode numbered 4 (the other force-feedback control mode) does
not require a similar consideration on account of it being
inherently bidirectional in terms of net electrostatic force,
although this mode will involve a background V.sub.fb to balance
the electrode gaps of electrostatic actuator 34 if these electrode
gaps are not inherently balanced. The presence of a large
background V.sub.fb will significantly alter the range of V.sub.fb
remaining to counter forces acting on conductive indenter 62. A
negative background V.sub.fb is preferable over a positive one
because a typical nanoindentation test involves attractive forces
that pale in comparison to the maximum in repulsive force. This
aspect should be considered when constructing actuatable capacitive
transducer 30.
[0140] As for load control, mode number 5 from the above list (an
open-loop approximation of load control) provides an advantage over
mode number 1 (true load control) in the sense that the former can
be initiated from the out-of-contact condition, whereas the latter
requires being in contact to achieve feedback loop closure. It is
desirable to have the option of initiating nanoindentation tests
from the out of condition (also a characteristic of modes numbered
2-4 and 6) in light of our quantitative in-situ TEM nanoindentation
results revealing a single nanograin of aluminum plastically
deforming upon first contact. Mode number 5, however, does have two
distinct disadvantages in comparison to mode number 1. Firstly, in
the case of mode number 5, the achieved F.sub.c will not exactly
match the desired F.sub.c, the usually small difference being
related to F.sub.s and the dependence of F.sub.e on .delta..
Secondly, open-loop modes of operation (mode number 6 included) do
not provide an opportunity to tune a feedback loop to damp
actuatable capacitive transducer 30 in the high-vacuum environment
of a TEM. As will be demonstrated, an optimally tuned feedback loop
dramatically decreases the settling time of actuatable capactive
transducer 30 in this very low damping medium.
[0141] As for mode number 6, it falls outside the domain of
quantitative nanoindentation on account of the series loading
configuration it adopts. Furthermore, this mode does not enable
dictating either a well-defined penetration depth rate or a
well-defined contact force rate, a significant drawback if testing
rate sensitive materials. Further, this mode is subject to the
well-known jump-to-contact phenomenon that can happen during
initial sample approach. Further still, this mode necessitates an
additional displacement sensor dedicated to measuring the extension
or contraction of 3D piezoelectric actuator 182 to achieve the best
possible performance. But in spite of these numerous difficulties,
mode number 6 still is useful because it is the mode most capable
of detecting extremely small forces, providing the electrostatic
actuation circuitry is disconnected from electrostatic actuator
34.
[0142] Switching between various nanoindentation operating modes
during a nanoindentation test is a possibility. For example, it is
feasible to start the nanoindentation test in the load control mode
(mode number 1) to maintain F.sub.c at a specific small repulsive
value for the purpose of measuring the rate of positional drift,
then switch to the displacement control mode (mode number 2) to
detach conductive indenter 62 from the sample by a specified
distance, then reengage the sample in the displacement control mode
(mode number 2) to the specific small repulsive value or to some
other repulsive value, then switch to the load control mode (mode
number 1) to increase F.sub.c to the desired maximum load and to
subsequently decrease F.sub.c to the specific small repulsive value
or to some other repulsive value, then switch to the displacement
control mode (mode number 2) to detach conductive indenter 62 from
the sample by a specified distance. This scenario allows for data
correction with regard to positional drift (see Reference 21), and
provides data possibly showing attractive interaction forces during
the reengagement step, and provides data for better establishing
the position of the sample's surface which defines the zero point
of the nanoindentation test (see Reference 21), and provides data
possibly showing adhesive forces (also attractive) as conductive
indenter 62 detaches from the sample for the final time, while
conducting the bulk of the nanoindentation test in the load control
mode (mode number 1). Of course, V.sub.1 must be greater than zero
before engaging the sample prior to the nanoindentation test in
order to have enough V.sub.1 in reserve to be able to chase
positional drift of either sign and to be able to guarantee the
ability to detach conductive indenter 62 from the sample. Here,
engaging the sample prior to the nanoindentation test involves the
use of 3D piezoelectric actuator 182 to displace actuatable
capacitive transducer 30 towards the sample until achieving the
specific small repulsive value.
[0143] The following Expression E.11 can be used to calculate the
contact force for the case of V.sub.1 intentionally greater than
zero before engaging the sample in conjunction with V.sub.2=0
throughout the nanoindentation test:
F c = .kappa. o [ 1 - ( .delta. ' + .delta. offset ) / d o ] 2 ( V
' + V offset ) 2 - .kappa. o ( 1 - .delta. offset / d o ) 2 V
offset 2 - k .delta. ' ; E .11 ##EQU00009##
where V.sub.offset is the value of V.sub.1 before engaging the
sample, V' is the change in V.sub.1 from V.sub.offset,
.delta..sub.offset is the value of .delta. owing to V.sub.offset,
.delta.' is the change in .delta. from .delta..sub.offset, and
where the remaining parameters have been defined already. In the
case of the single-sided force-feedback control mode (mode number
3), the value of V' is whatever is necessary to maintain .delta. at
zero. The necessity of knowing both .kappa..sub.o and d.sub.o in
this case stems from the need to calculate the term
.kappa. o ( 1 - .delta. offset / d o ) 2 ##EQU00010##
for any chosen value of V.sub.offset. The instrument's software
treats V.sub.offset as an adjustable parameter to allow the user to
balance having a sufficient reserve in V.sub.1 against shrinking
the range of V'.
[0144] Returning to the jump-to-contact phenomenon, conductive
indenter 62 will jump into contact with the sample if the gradient
of the attractive force acting on conductive indenter 62 exceeds
the spring constant of actuatable capacitive transducer 30. The
occurrence of jump-to-contact prevents force-displacement
measurement over the entire range of indenter-sample separation.
Mode number 5 also is subject to the jump-to-contact phenomenon,
whereas mode numbers 2-4 are stable against jump-to-contact on
account of the displacement control they provide. However, no mode
can stop atoms of the sample's surface from jumping into contact
with conductive indenter 62 if they desire to do so. As for mode
number 1, the jump-to-contact phenomenon is irrelevant because mode
number 1 requires being in repulsive contact before being
initiated.
[0145] The combination of nanoindentation head 180, which comprises
actuatable capacitive transducer 30 and 3D piezoelectric actuator
182, TEM holder 203, and nanoindentation head 180 control system
220 helps define a quantitative in-situ TEM nanoindenter. Numerous
performance aspects of a built quantitative in-situ TEM
nanoindenter were investigated in a JEOL JEM 3010 TEM located at
NCEM/LBNL over the time period of Mar. 23-25, 2005. NCEM/LBNL is a
facility of the Department of Energy and a confidentiality
agreement is in place with this facility. Unless indicated
otherwise, the performance results that follow were obtained in
this particular TEM. Obviously, all components specified in the
description of the performance results are built components.
[0146] To quantify baseline noise characteristics, out-of-contact
force and displacement vs. time traces were acquired in a
measurement bandwidth typical of nanoindentation tests. From these
traces, the out-of-contact force noise floor was estimated to be
0.11 .mu.N RMS while using the open-loop mode with V.sub.1=0, and
0.16 .mu.N RMS while using the displacement control mode with the
demanded .delta. kept constant. From the same traces, the
out-of-contact displacement noise floor was estimated to be 0.41 nm
RMS while using the open-loop mode, and 0.48 nm RMS while using the
displacement control mode. These values are considerably above the
limits for thermally-driven mechanical noise in the same
measurement bandwidth, yet are indicative of a high-performance
nanoindenter. The out-of-contact noise floors were not affected by
the status of the 300 kV electron beam (impinging the conductive
indenter vs. turned off) or by the choice of magnification mode
(low vs. high).
[0147] Use of the displacement control mode caused a moderate
increase in the out-of-contact noise floors; however, this mode and
the other modes invoking feedback were extremely beneficial in
terms of improving the time to settle after encountering a
transient disturbance. FIG. 10A illustrates an out-of-contact
impulse-ring-down trace 250 for the open-loop mode (V.sub.1=0) with
the vacuum pressure in the range of 10.sup.-7 torr. Based on the
exponential decay of the trace's envelope, the Q in high vacuum is
6000 in comparison to only 25 in an air environment. As a
consequence, the elapsed time to a 99% settled displacement signal
is an unacceptably long 66 s. FIG. 10B provides an out-of-contact
step-response trace 252 while using the displacement control mode
with the vacuum pressure in the range of 10.sup.-7 torr; a step
change in the demanded .delta. initiated the step response. The
benefit of closed-loop operation is clearly evident in that the
elapsed time to a 99% settled displacement signal is reduced from
an unacceptably long 66 s to a mere 13 ms.
[0148] A hand turning any of coarse positioning screws 210 of the
TEM holder 200 was found to be a significant source of potentially
damaging transients. On several occasions, conductive indenter 62
visibly damaged the sample while coarse positioning, the result of
high-amplitude ringing in high vacuum set off by the action of the
hand. Of note, all such occurrences corresponded to using the
open-loop mode. Apparently, closed-loop control prevented large
swings in indenter displacement even during the rough act of coarse
positioning. Closed-loop control also suppressed ringing following
a sudden change in how a sample responded to a nanoindentation
test.
[0149] The stability of the natural state of displaceable
electrodes 42 against rotation of TEM holder 200 about its central
axis was tested over the physically possible range of 0-28.degree..
The change in the displacement signals was only 46.8 nm over the
full range of rotation, which indicated an extremely horizontal
alignment with respect to gravity. The stability of the natural
state also was tested against the status of the electron beam. The
electron beam impinging conductive indenter 62 did not affect the
displacement signals relative to their values with the electron
beam turned off. However, the displacement signals were noticeably
impacted by the choice of magnification mode. Switching from low to
high magnification mode reproducibly caused the displacement
signals to shift by an amount corresponding to 1.03 .mu.m towards
the electron beam. Fortunately, the shift was invariant as long as
the magnification mode remained unchanged.
[0150] A shift by 1.03 .mu.m is not unacceptable, but does require
onsite re-determination of the electrostatic force calibration
function for certain nanoindentation operating modes. The
instrument's software possesses an algorithm designed to optimize
the electrostatic force calibration function so that post-shift,
out-of-contact force-displacement curves will yield the proper
value for k. A shift significantly much greater than 1.03 .mu.m
would be intolerable, especially for the case of the double-sided
force-feedback control mode.
[0151] The displacement signals in the low magnification mode were
comparable to their values for horizontal alignment outside the
TEM. This observation is consistent with a weak to nonexistent
local magnetic field when in the low magnification mode, and a
strong local magnetic field when in the high magnification mode.
Trace levels of ferromagnetic impurities in components of
actuatable capacitive transducer 30 likely participated in the
coupling to the magnetic field. The titanium shaft of conductive
probe 60 possesses by far the highest ferromagnetic content in
terms of concentration, iron impurities at the level of 0.3 wt %,
and in terms of total number of ferromagnetic atoms. Hence, an
ultrapure titanium shaft might substantially reduce coupling to the
magnetic field.
[0152] FIG. 11A illustrates one embodiment of an electrical
configuration 260 found to be compatible with the JEOL JEM 3010 TEM
for bleeding charge from conductive indenter 62. As can be seen in
FIG. 11A, conductive indenter 62, the remainder of conductive probe
60, conductive threaded rod 48, and a probe wire 262 soldered to
the probe wire tab 56 in intimate electrical contact with
conductive threaded rod 48 form an electrical path to TEM holder
200. FIG. 11A also shows a sample 264 electrically connected to TEM
holder 200 to ensure that the sample and conductive indenter 62 are
nominally at the same electrical potential, via good electrical
continuity between sample clamp 212 and the point at which the
probe wire attaches to TEM holder 200. Probe wire 262 must be
highly flexible in order to not impede the motion of displaceable
electrodes 42.
[0153] TEM holder 200 could not be grounded to control system 200
of nanoindentation head 180 as doing so sounded an alarm
originating from the TEM. However, electrically connecting the
conductive transducer body 32 of actuatable capacitive transducer
30 and ground planes 84 to the ground of control system 220 did not
sound the alarm because these components were kept electrically
isolated from TEM holder 200. Apparently, electrically connecting
TEM holder 200 to the ground of control system 220 is interpreted
by the TEM as a crash of TEM holder 200 into a pole piece.
[0154] FIGS. 11B and 11C show force-displacement curves 270 and 272
while using the displacement control mode, which correspond to
conductive indenter 62 first approaching then withdrawing from the
tip of a plank-type silicon AFM cantilever while the TEM imaged
both conductive indenter 62 and the tip of the cantilever. The
curve in FIG. 11B illustrates the detrimental impact of not
electrically connecting conductive indenter 62 to a charge sink of
any type, whereas the curve in FIG. 11C is an example of a proper
mechanical response. Measuring a proper mechanical response
required both conductive indenter 62 and the AFM cantilever
(product no. NSC15/No Al from .mu.masch) being nominally at the
same electrical potential.
[0155] In FIG. 11B, the significant attractive (negative) forces
seen in the initial portion of the approach segment likely are the
consequence of conductive indenter 62 and the AFM cantilever
absorbing different amounts of charge from the electron beam. The
subsequent lack of attractive forces throughout the withdrawal
segment likely is evidence for charge equilibration once repulsive
contact (yielding positive forces) has been made. Interestingly,
the observation of at least two discrete decreases in attractive
force during the initial portion of the approach segment is
suggestive of discrete charge transfer events occurring prior to
making repulsive contact. FIG. 11C, in comparison, does not show
significant attractive forces over any portion of the curve.
Moreover, the approach segment data and the withdrawal segment data
in FIG. 11C are virtually identical. Apparently, TEM holder 200
serves as a sufficient charge sink even when not electrically
connected to the ground of control system 220 of nanoindentation
head 180.
[0156] To ascertain the ability of actuatable capacitive transducer
30 to maintain its metrological accuracy in the TEM environment, a
number of force-displacement curves while using the displacement
control mode were acquired with conductive indenter 62 against the
tip of the AFM cantilever while imaging with the TEM. The initial
slope of these force-displacement curves was consistent with an AFM
cantilever spring constant of 50.6.+-.0.8N/m at the tip location.
In comparison, a value of 50.9N/m at the tip location was obtained
by inputting the AFM cantilever's dimensions (measured from SEM
images) into the well-known cantilever bending equation. The high
level of agreement between measured and calculated AFM cantilever
spring constants indicated the TEM environment did not impact the
metrological accuracy of actuatable capacitive transducer 30.
[0157] The following is an example of methodology preceding
quantitative in-situ TEM nanoindentation tests on wedge-shaped
samples, such as wedge-shaped sample 264 depicted in FIG. 11A,
which have a plateau generally in the range of 100 nm in width and
macroscopic dimension in length. First, TEM holder 200 is
translated and rotated to achieve optimized TEM images of sample
264. Next, the TEM's magnification is adjusted to provide a large
enough field of view such that both conductive indenter 62 and
sample 264 can be seen at the same time. Next, coarse positioning
screws 210 of TEM holder 200 are adjusted to bring conductive
indenter 62 close enough to sample 264 to be well within the range
of motion of 3D piezoelectric actuator 182, while adjusting the
TEM's magnification as needed. Any of the variations of
displacement control can be used during coarse positioning to
prevent large swings of displaceable electrodes 42 in response to
the action of the hand adjusting coarse positioning screws 210.
Next, 3D piezoelectric actuator 182 is used to position conductive
indenter 62 to within a nanoscale distance to a point on the
plateau centered with respect to the plateau's width, again
adjusting the TEM's magnification as needed, The desired
nanoindentation operating mode, usually one of the variations of
displacement control, can be selected during this process of fine
positioning. Next, the nanoscale gap between conductive indenter 62
and the plateau is observed for a period of time to ensure that it
is stable. Once found to be stable, the nanoindentation test is
initiated to indent the selected point on the plateau centered with
respect to the plateau's width. Conducting a nanoindentation test
in the load control mode (mode number 1) requires using 3D
piezoelectric actuator 182 to place conductive indenter 62 in
minimal repulsive contact with the plateau before initiating the
nanoindentation test.
[0158] The following is a first example of quantitative in-situ TEM
nanoindentation results that demonstrate the quantitative in-situ
TEM nanoindenter's capability of investigating fundamental aspects
of nanoscale material deformation. FIGS. 12A and 12B provide two
examples of force-displacement curves 280 and 282 corresponding to
a boron-doped diamond indenter of the Berkovich geometry indenting
a nanograin of an aluminum film deposited on a wedge-shaped,
single-crystal silicon substrate. Curve 280 in FIG. 12A was
acquired while using the displacement control mode, whereas curve
282 in FIG. 12B was acquired while using the single-sided
force-feedback control mode. Both curves 280 and 282 are dominated
by repulsive forces, but both indicate relatively strong attractive
adhesive forces during the final act of withdrawing conductive
indenter 62 from the aluminum nanograin.
[0159] Signals digitized during a nanoindentation test can include
signals indicative of electrostatic actuation voltage, signals
indicative of displaceable electrode displacement, and a signal
indicative of the extension or the contraction of z segment 188 of
3D piezoelectric actuator 182. Time also is recorded. The TEM
images provided in FIG. 12C correspond to two video frames 284 and
286 extracted from a stream of TEM images recorded during the
process of acquiring the force-displacement curve 280 in FIG. 12A.
Left hand video frame 284 of FIG. 12C shows the aluminum nanograin
about to be indented to be initially dislocation free, whereas
right hand video frame 286 of FIG. 12C shows that dislocations
confined to the aluminum nanograin on account of a difficulty in
traversing the grain boundary have been nucleated and multiplied
during the process of nanoindentation.
[0160] Focusing on force-displacement curve 280 of FIG. 12A, there
are several discrete load drops that occur during the process of
increasing the penetration depth, where each discrete load drop
corresponds to sudden stress relaxation accompanying a sudden
change in the aluminum nanograin's subsurface dislocation
structure, as indicated by time correlation of the
force-displacement curve to the recorded stream of TEM images. This
particular experimental result is the first to conclusively link
discrete load drops to discrete dislocation nucleation and
multiplication events. However, surprisingly, the first large
discrete load drop, indicated at 290, is not the one associated
with the onset of plasticity, an observation at odds with the
belief of many researchers. Instead, the onset of plasticity is
coincident with the small force transient, indicated at 292. Video
frames 284 and 286 provided in FIG. 12C are sequential video frames
of this initial dislocation nucleation and multiplication event.
The conclusion reached here would not have been possible without
having both a force-displacement curve and an associated
time-correlated stream of TEM images.
[0161] As for force-displacement curve 282 of FIG. 12B, it
corresponds to a different aluminum nanograin, yet is similar to
force-displacement curve 280 of FIG. 12A in terms of overall
characteristics. However, force-displacement curve 282 of FIG. 12B
is obviously an improvement over force-displacement curve 282 of
FIG. 12A in terms of transducer control performance. For example,
the discrete load drops are more crisp in curve 282 of FIG. 12B.
Unfortunately, the lack of a displacement sensor dedicated to
measuring the extension or the contraction of z segment 188 of 3D
piezoelectric actuator 182 deems force-displacement curve 282 of
FIG. 12B not fully quantitative, although 3D piezoelectric actuator
182 is found to behave more ideally in high vacuum than in air.
[0162] The following is a second example of quantitative in-situ
TEM nanoindentation results that demonstrate the quantitative
in-situ TEM nanoindenter's capability of investigating fundamental
aspects of nanoscale material deformation. FIG. 13A provides a
force-displacement curve 300 corresponding to the same conductive
indenter 62 indenting an initially dislocation-free section of the
plateau of a wedge-shaped, single-crystal silicon sample not having
a film. This nanoindentation test was run in the displacement
control mode, and involved a loading segment at a constant
displacement rate, followed by a holding segment at a constant
penetration depth, followed by an unloading segment at a constant
displacement rate. The corresponding time-correlated stream of TEM
images indicated an initial period of elastic contact followed by
continuous dislocation activity during the remainder of the loading
segment, but in contrast to the aluminum nanograins, load drops
were not observed.
[0163] During the holding segment, stress relaxation gradually
occurred even though both the contact area and the
nanoindentation-induced dislocation structure seemed to be static.
Nothing noteworthy occurred during the unloading segment until
experiencing a strong attractive adhesive force (35 .mu.N in
magnitude) during the final act of withdrawing the conductive
indenter from the sample. At this point, conductive indenter 62 was
kicked out suddenly from the sample which forced the control loop
to fight back to recover the proper value of displacement in time.
This kick-out event is indicated in FIG. 13a by the sequence of
arrows. Finally, one more kick-out event occurred before completing
the unloading segment, again starting from an attractive adhesive
force. The corresponding time-correlated stream of TEM images
confirmed the kick-out events being rather violent in nature.
[0164] FIG. 13B provides a post-mortem TEM image 302 of the
residual deformation zone as well as three post-mortem electron
diffraction patterns. Diffraction pattern 304 in the lower left
hand corner corresponds to the diamond cubic crystal structure of
pristine silicon, nanobeam diffraction pattern 306 in the upper
left hand corner also corresponds to the diamond cubic crystal
structure but comes from the heavily dislocated region of the
residual deformation zone, and nanobeam diffraction pattern 308 of
amorphous character in the upper right hand corner comes from the
surface pile not present before the nanoindentation test.
Apparently, tensile stresses associated with adhesive forces were
enough to trigger sudden volume-expanding phase transformations
from plastically-deformed, diamond-cubic silicon to amorphous
silicon. This particular experimental result raises the interesting
possibility of a method that entails viewing/recording the
evolution of the nanobeam diffraction pattern throughout the
nanoindentation test in order to monitor the local crystal
structure as a function of the force-displacement curve.
[0165] The following concludes the description of the in-TEM
performance results: [0166] 1. Actuatable capacitive transducer 30
was stable against the snap-to-contact instability over the
software-permitted displacement range of 5 .mu.m. [0167] 2.
Actuatable capacitive transducer 30 was stable against the
spark-gap instability over the range of electric field strength
needed to conduct the tests. [0168] 3. Corona discharge was not
observed. Neither actuatable capacitive transducer 30 nor 3D
piezoelectric actuator 182 (also a high voltage device) received
power until achieving high vacuum. [0169] 4. TEM images did not
provide evidence for conductive indenter 62 charging up even when
an electrical path from conductive indenter 62 to TEM holder 200
was not provided. This observation suggests force-displacement
curves are more sensitive to charging than TEM images. [0170] 5. In
general, the quantitative in-situ TEM nanoindenter did not exhibit
positional drifts large enough to be detected at the magnifications
necessary for the tests. Drifting relative to the TEM image's field
of view can be ascertained by directly observing the position of
conductive indenter 62 and the position of the sample during
periods of idle. [0171] 6. Although a value for the load frame
stiffness was not determined, nothing indicated a load frame
stiffness problem. [0172] 7. Pumping down the fully-assembled TEM
holder after plasma cleaning took approximately 1 hour. In
comparison, pumping down the TEM holder 200 prior to receiving the
assembly comprised of the internal tube 206, 3D piezoelectric
actuator 182, and actuatable capacitive transducer 30 took only
about 5 minutes. Although a pump-down time of approximately 1 hour
is not intolerable, adding vents to the internal tube should result
in an improvement. [0173] 8. It is not trivial to properly position
conductive indenter 62 with respect to a wedge-shaped sample's
plateau because the electron beam transmits through the sample and
conductive indenter 62 regardless of whether conductive indenter 62
or the sample is in the foreground relative to the other. A
scanning probe microscopy method of imaging in the manner of an AFM
but using the indenter rather than a tip on a cantilever, to image
the topography of the plateau and the transitions to the sample's
side slopes, would be advantageous because such an image could be
used as a guide for refining the position of conductive indenter 62
with respect to the plateau, although the process of imaging might
damage the sample. In the event of sample damage, the
three-dimensional topography image could be used to predict how
much to offset 3D piezoelectric actuator 182 in all three spatial
dimensions to properly position conductive indenter 62 with respect
to a nearby undamaged section of the plateau without contacting the
sample. Post-test imaging in the manner of an AFM also enables
highly complementary three-dimensional and plan-view images of the
residual deformation zone. Imaging in the manner of an AFM could be
based on feedback involving z segment 188 of 3D piezoelectric
actuator 182 to maintain either a constant spring force if
actuatable capacitive transducer 30 is passive during imaging or a
constant transducer control effort if actuatable capacitive
transducer 30 is active during imaging. The former involves a
single feedback loop, whereas the latter involves one feedback loop
nested in another, the transducer control loop being the nested
loop.
[0174] The following begins a description of several embodiments of
the present invention. In a preferred embodiment of actuatable
capacitive transducer 30, electrostatic actuator 34 rather than the
capacitive displacement sensor 36 is closest to conductive indenter
62. In an alternative embodiment of actuatable capacitive
transducer 30, capacitive displacement sensor 36 rather than
electrostatic actuator 34 is closest to conductive indenter 62. An
advantage of electrostatic actuator 34 being closest to conductive
indenter 62 is that such an arrangement effectively shortens a
length of coupling shaft 46 which is potentially under high load.
However, it has been determined that force-displacement curves do
not noticeably depend on whether electrostatic actuator 34 or
capacitive displacement sensor 36 is closest to conductive indenter
62.
[0175] In the preferred embodiment of actuatable capacitive
transducer 30, having both first and second multi-plate capacitors
34 and 36 functioning as capacitive displacement sensors might seem
redundant at first glance. The reason for electrostatic actuator 34
also functioning as a capacitive displacement sensor has been
explained, but not the reason for having a multi-plate capacitor
functioning solely as a capacitive displacement sensor. Prior-art
actuatable capacitive transducers have been used to conduct dynamic
forms of nanoindentation testing as well as dynamic forms of
imaging in the manner of an AFM (see References 37-39). However, it
is difficult to suppress an oscillatory electrostatic actuation
voltage from feeding through, i.e., a portion of the oscillatory
electrostatic actuation voltage will appear in the displacement
signal if the displacement signal originates from the multi-plate
capacitor experiencing the oscillatory electrostatic actuation
voltage. This undesirable dynamic feedthrough effect increases in
severity with increasing oscillation frequency. Hence, a
multi-plate capacitor functioning solely as a capacitive
displacement sensor provides means for obtaining a displacement
signal free of dynamic feedthrough. This explanation leads to
another alternative embodiment of actuatable capacitive transducer
30, wherein one multi-plate capacitor functions solely as a
capacitive displacement sensor and another multi-plate capacitor
functions solely as an electrostatic actuator, if one is willing to
forego the double-sided force-feedback control mode.
[0176] Yet another alternative embodiment of actuatable capacitive
transducer 30 involves both first and second multi-plate capacitors
34 and 36 functioning as electrostatic actuators to increase the
load capacity, and at least one of first and second multi-plate
capacitors 34 and 36 functioning as a capacitive displacement
sensor, if one is willing to forego dynamic forms of
nanoindentation testing/imaging not corrupted by dynamic
feedthrough. Of course, it is also feasible to incorporate more
than two multi-plate capacitors into actuatable capacitive
transducer 30 to yield many possible combinations of multi-plate
capacitors functioning as electrostatic actuators and capacitive
displacement sensors. Any capacitor being used solely as an
electrostatic actuator can be a two-plate capacitor rather than a
three-plate type of a multi-plate capacitor.
[0177] In the preferred embodiment of actuatable capacitive
transducer 30, conductive threaded rod 48 is utilized to
electrically connect conductive probe 60 to the remainder of the
electrical path responsible for bleeding charge from conductive
indenter 62. It is possible to eliminate the need for conductive
threaded rod 48 being integral to the electrical path if the probe
wire 262 is electrically connected to conductive probe 60 instead,
but this is a far more cumbersome solution than the one
implemented. Nevertheless, attaching a probe wire to conductive
probe 60 is within the scope of the present invention. Eliminating
the capacitive displacement sensing function of electrostatic
actuator 34 would allow displaceable electrode 42 of electrostatic
actuator 34 to be grounded. Conductive threaded rod 48 in
electrical contact with the grounded displaceable electrode would
prevent conductive indenter 62 from charging up. However, in the
case of the JEOL JEM 3010 TEM, this would require sample clamp 212,
being electrically isolated from TEM holder 200, to be grounded as
well and to avoid sounding the TEM's alarm in the event the
electrical conductivity of the indenter-sample contact increased
sufficiently. Furthermore, electron beam current passing through
displaceable electrode 42 of electrostatic actuator 34 might cause
enough noise to be evident in force-displacement curves.
Electrically isolating sample clamp 212 from TEM holder 200 does
raise the interesting possibility of electrically biasing the
sample relative to conductive indenter 62 to measure the electrical
conductivity of the indenter-sample contact. But this would be
problematic if conductive indenter 62 was electrically connected to
displaceable electrode 42 of electrostatic actuator 34 because then
displaceable electrode 42 would be increasingly shorted to the
sample bias as the electrical conductivity of the indenter-sample
contact increased.
[0178] Other feasible but non-exhaustive modifications to
embodiments of the present invention described herein include
significantly shortening the portion of coupling shaft 46 external
to conductive transducer body 32, pairing each spring of springs 44
with a mirror image spring, adding a lock-in amplifier to control
system 220, and motorizing coarse positioning screws 210. In one
scenario, the preferred embodiment of actuatable capacitive
transducer 30 could be used for horizontal applications outside a
TEM, but it would not be suitable for vertical applications on
account of gravity's effect on the relatively high sprung mass.
Significantly shortening coupling shaft 46 to sufficiently reduce
the sprung mass would allow actuatable capacitive transducer 30 to
be used in vertical applications, although this likely would render
actuatable capacitive transducer 30 useless in a TEM. Pairing each
spring of springs 44 with a mirror image spring would eliminate any
tendency of displaceable electrodes 42 to rotate while being
displaced, but these additional springs would complicate achieving
a relatively low overall spring constant. Adding a lock-in
amplifier to control system 220 to measure the amplitude and the
phase shift of the oscillatory component of the displacement signal
of capacitive displacement sensor 36 during dynamic excitation
would facilitate dynamic forms of nanoindentation testing/imaging.
Motorizing coarse positioning screws 210 would eliminate the large
transients caused by the action of the hand turning the screws, and
would enable motor-assisted hunting of the sample's surface in the
manner of an AFM. This concludes the description of several
embodiments of the invention in addition to the preferred
embodiment.
[0179] Although specific embodiments have been illustrated and
described herein, it will be appreciated by those of ordinary skill
in the art that a variety of alternate and/or equivalent
implementations may be substituted for the specific embodiments
shown and described without departing from the scope of the present
invention. This application is intended to cover any adaptations or
variations of the specific embodiments discussed herein. Therefore,
it is intended that this invention be limited only by the claims
and the equivalents thereof.
* * * * *